This is something, she says, that Tony used to do a lot. She calls him by his first name as though they're old friends. As though their relationship was not slightly more complex than that.

"We often attended breakfasts and things together," she says. "And you would get these glasses of water with ice in them. We would have microphones on us, and you would just hear this..."

Here, the former prime minister breaks off to imitate the sound of her fellow former prime minister crunching ice. She really commits to it. The sound effect is surprisingly realistic - coming from the back of her throat, it neatly conjures Abbott's unique blend of machismo and eccentricity. She laughs.

"Sometimes I would have to lean over and put my hand on his arm and say, 'Tony, I just cannot listen to you crunching that ice,'" she says.

Gillard is not supposed to be doing impressions, or talking at all. She is supposed to be posing for the Good Weekend photographer, but she is so relaxed, and so affable, that she is easily drawn into conversation about the past, even though the plan is to talk about her present, and her future.

She chats to the hairstylist about Wales, where she was born, and to the photographer about the pearl necklace she's wearing. She chats about the films she's watched on her frequent long-haul flights (Aquaman, Dumplin', On the Basis of Sex, Vice). She chats about the upcoming national vote. She's a "nervous Nellie" about elections, she says, and is taking nothing for granted. She remarks that the campaign has become a referendum on the Labor opposition, rather than the more traditional one on the government. She turns out, as we all know, to be right.

Gillard is engaged with the election but shows no sign of being tense about it. Politics is not her problem any more. Plus, as she puts it, "personality-wise, I've always been on the even-keel side".

This temperament helps explain how she's traversed the tricky terrain into a post-PM life. Where some former leaders have fallen into bitterness or spite, or become what another one-time PM, Malcolm Turnbull, called "miserable ghosts" who leak and quibble and spook their parties from the shadows, Gillard has displayed minimal outward angst or interference in her party's politics, nor felt the need to put her two cents' worth in on national issues. To the contrary, her new life looks a lot like liberation.

She works in various roles representing what she calls the "golden threads" of her prime ministership: education, women's leadership and mental health. She jets around the world giving speeches on gender and leadership, including hosting Q&As with her friend Hillary Clinton and visiting Africa with pop star Rihanna, her new BFF (more on that later).

Gillard weathered severe criticism during her time as Australia's first female prime minister, a position she held from 2010 to 2013, and Australians of all political persuasions have strong views on her time in power.

Many point out that when she knocked off Kevin Rudd in 2010, she started the deeply unpopular trend for ousting sitting prime ministers (one which saw him return the favour a few years later). Some think she cynically used her gender to explain away poor leadership.

Those within the LGBT+ community revile the way she opposed same-sex marriage, and some recall how she pushed thousands of welfare-dependent single parents onto the lower Newstart payment.

Be all that as it may, it feels as if something has shifted in attitudes towards her, sparked in no small part by the global wave of feminism that crystallised in the #MeToo movement, and in a national discussion of everything from female representation in politics to domestic violence and sexual relations between the genders.

It's almost as if the times have caught up with the one-time Labor PM, who made an international name for herself in 2012 with her famous misogyny speech. The upshot is that in the six years since she left the Lodge, Julia Gillard has become something of an international poster child for female empowerment.

This has led to a reassessment of her short but productive tenure back home, during which she established the National Disability Insurance Scheme (NDIS), instituted the Gonski education reforms, and set up the Royal Commission into Institutional Responses to Child Sexual Abuse (Gillard has the highest rate of passing legislation of any Australian prime minister, above even that great reformer, Bob Hawke). In that reappraisal, many Australians have been reflecting on how she was treated as PM, and how she has behaved since.

"I don't think there's any doubt that the work she does, and the public stance she has taken, has been very different to a range of very recent incumbents who have occupied the post of prime minister," says former Victorian premier Jeff Kennett, the Liberal who recruited Gillard for one of her current gigs as the chair of mental health organisation, Beyond Blue.

Former Labor Victorian premier Steve Bracks, a long-time friend of Gillard, goes further, saying she's a "model of a past prime minister on how to act, what to get involved in". He adds: "She's conducted herself with great dignity and great gravitas. She's kept out of [political] issues largely and that's probably a good thing, and it's probably a lesson for others to follow in the future."

It could be an act, but Gillard does not look bitter and does not talk as though she is. Here, high above the Sydney CBD at the UNSW's Centre for Ideas, where she's just participated in a panel talk about gender equality, the former PM chats so volubly that our photographer tells me to stop distracting her so he can get his shot. Afterwards, both he and the hairstylist ask for a photo with her.

As I discovered two nights earlier, at a sold-out Centre for Ideas Q&A she gave at the Sydney Town Hall - an event that ended with a standing ovation from the 2000-strong crowd, during which one excited attendee shouted, "You did so well, Julia!" - Julia Gillard fandom is real, and it is strong.

A few weeks after the photo shoot, I arrange to meet Gillard at the Grand Hyatt in Melbourne, where she's staying for a few days to attend board meetings for CVS Lane, a boutique finance and investment house, and to take an afternoon tea with some Werribee Tigers footy fans who won an auction prize to meet her.

She lives in Adelaide now, near her family - sister Alison, niece Jenna and husband Damien, their children Ethan and Isla, her nephew Tom and his wife Laura - but is in Melbourne frequently for board commitments, and to see friends and her partner Tim Mathieson, the former first bloke.

The couple don't live together, but meet up frequently in the southern capital, where they stay in a dog-friendly Airbnb (Reuben, the former first dog, is now eight years old). Otherwise, Mathieson spends his time on a block of land the couple owns in country Victoria.

I wait for Gillard in the hotel lobby, accompanied by her media adviser, one of the three staff she's entitled to as a former prime minister. On the stroke of the hour, the 57-year-old emerges, rising up on the escalator from the lower floor, serene in bottle-green.

She is warm and physically unchanged from her PM days. Seeing her in person feels familiar and strangely comforting, although tinged with something else - something darker that may be guilt, or bad memories from the ugly seam of misogyny her prime ministership cracked open in this country.

I am reminded of Sydney broadcaster Alan Jones's call to "shove her and Bob Brown in a chaff bag and take them as far out to sea as they can" and I am reminded of the talkback caller to Jones's program who asked, "Does she go down to the chemist to buy her tampons or does the taxpayer pay for them as well?" (Another called her a "menopausal monster", so she really couldn't win.)

I'm reminded of the fundraiser for LNP candidate Mal Brough which had "Julia Gillard Kentucky Fried Quail" on the menu - "small breast, huge thighs and a big red box". I'm reminded of how the Herald Sun called her "coquettish" and "giggling" when she hosted US president Barack Obama, and how the epithet of "liar" was weaponised against her - she didn't just lie, she personified lying. She was Juliar.

I am also reminded of how many people - in the media and in public life - ignored or explained away the sexism levelled against her at the time. I am reminded that I was one of those people.

"Hullo!" says Gillard cheerfully, leading us to the elevator and using her swipe card to get us up to the VIP lounge on the 31st floor. We settle down for tea at a round table with expansive views over the Melbourne skyline.

The shock Labor federal defeat is two days old, so I begin by asking her about it - she watched the coverage at home in Adelaide, with a few family members and white wine - and what role, if any, she had in advising Shorten. Labor leader since 2013, Shorten was one of the pivotal factional players who installed Gillard as PM in 2010, and helped boot her for Kevin Rudd a few years later. She spoke to Shorten a couple of times during this year's campaign, "broad-brushstroke conversations", she says.

"I don't publicly loom up with my view. I don't ring and press my views but if people want to talk to me, I'm available to put a perspective. Various members of the Labor team do avail themselves of that opportunity. I don't ever want it to be ever more than that." She pauses. "Yeah. That's, I think, the appropriate position for a former prime minister."

As it turned out, Gillard was of use to Shorten in another way, speaking to him the day after his election loss, when she was able to offer "an insight into how devastated he would be personally".

When Gillard lost to Rudd, she retreated to the Melbourne suburb of Altona and holed up in the unprepossessing home in which she had once been photographed with her empty fruit bowl (she explained in her 2014 memoir that it was a decorative bowl and not meant to be functional).

It was during those days that she started thinking about what to do post-politics. Her first order of business was writing that memoir, My Story, which sparked a bidding war between publishers and went on to sell just over 80,000 copies (Ever the girly swot, Gillard handed her 170,000-word draft in on time.)

She also signed up to US talent outfit The Harry Walker Agency. Six years on, she gives about 40 talks a year, including at commercial events (industry pundits estimate she'd be paid about $40,000 per speech), those for various official roles, and gratis efforts for worthy causes.

In the past year, she's spoken in Mumbai and Salt Lake City about women's leadership, in North Carolina and California on the Asian century, and in Connecticut on diplomacy and leadership in the age of disruption.

"It's almost stage acting - 'performance' is the right word," she says of the commercial speaking engagements. "They want to hear your life experiences and how you dealt with them, so it's gender, it's resilience ... often I'm asked about gun laws, because the Australian example is so noted in the US. They ask about China."

Internationally, Gillard has a host of more formal roles. She's a distinguished senior fellow with the Centre for Universal Education at the Brookings Institution in the US; patron of the Campaign for Female Education (for which she sat on a panel with a pregnant Meghan Markle in March); and has worked with her friend Hillary Clinton on a female-education initiative called CHARGE; as well as interviewing her on stage when the former US secretary of state toured here.

Perhaps her most high-profile role is as chair of the Global Partnership for Education (GPE), which specialises in improving access to education, and lifting its quality, for the world's poorest children. Funded through philanthropy and the foreign aid budgets of more than 20 nations, it is active in 68 developing countries.

Last year, she also became inaugural chair of the Global Institute for Women's Leadership at prestigious King's College London. The institute was Gillard's brainchild - while she was writing her memoir, she realised there was a shortage of high-quality global research on women as leaders, and the ways in which gender impacts perceptions of leadership. She wanted to fill the gap, so approached King's with the idea. The gig currently involves her spending three months a year in London.

"They are all close to my heart," she says of her international portfolio of roles.

"The travel can be gruelling, and the workload is high, but post-politics I have a unique opportunity to use my profile and experience to advocate for global change in two areas I have been passionate about my whole life: education and gender equality."

When at home, she's kept busy with a raft of positions, including as visiting professor at Adelaide University; as patron of the John Curtin Prime Ministerial Library in Western Australia; and with Beyond Blue, where she's been a board member since 2014, and replaced Jeff Kennett as chair in 2017.

"I was searching around for a person who would be able to cut through the clutter that exists in the media, and would be able to open doors at a state and federal political level if necessary," Kennett explains.

"She is simpatico with our work; her dad worked as a psychiatric nurse, and she established the NDIS. She thought it through and eventually agreed. The organisation is in excellent hands."

Gillard even has her own podcast. In introducing A Podcast of One's Own with Julia Gillard to the world via Instagram last month, she wrote that gender discrimination had "raised its ugly head" during her prime ministership, something she was "taken aback" by.

She went on to say she was "still offended by the lack of women in leadership", hence "decided to make a podcast about it".

In 2017, Gillard was in Hamburg for the Global Citizen Festival, a huge annual pop concert staged by a youth-oriented movement founded by 36-year-old Australian Hugh Evans. Global Citizen is a partner of Gillard's Global Partnership for Education (GPE), which means, among other things, that she mixes with a lot of celebrities - often without realising it.

"I was this far away from saying, 'And what do you do?'," she says of the "very nice young man" with an American accent she chatted to in a hotel lift in Hamburg.

"And then I realised the huge guy next to him was probably security. And then I realised there was a slight frisson in the lift. So I got out of the lift and worked out later that it was, um ..." She hesitates, trying to recall the name. Eventually she lands on it. "Pharrell!"

"Williams?" I say. "Pharrell Williams."

Yep, the RnB pop star with 10 Grammy awards.

It was Hugh Evans who set Gillard up with Rihanna, the internationally famous pop star. Rihanna was interested in becoming an ambassador for the GPE, but wanted to meet Gillard before making up her mind. The pair met for drinks at a restaurant in New York's SoHo in 2016.

"We had a really interesting conversation," Gillard recounts. "She was very interested in [me] being the first woman [PM]. She's very interested in perspectives on feminism and women's leadership. We ended up talking about some of the psychological research there is now around women's leadership.

"She told me about why she was interested in education, which is very much from her own experience; she was discovered at 14 so she didn't complete her own education. She thinks it's very valuable. And so it was sort of easy, and that's continued to be my experience with her."

In 2017, Gillard, Evans and Rihanna - plus Rihanna's entourage - travelled to Malawi in south-east Africa to highlight the need to educate young girls from the poorest backgrounds.

Staying in a hotel together, they went on day trips to village schools, where the differing reactions were interesting. In the high schools, Rihanna was recognised, and mobbed by overjoyed schoolgirls.

In the primary schools, however, it happened less often, "and I think she finds some sort of exuberant freedom in that, too". The exuberance comes through in the photos and video from that trip, where Rihanna dances, claps and sings with the children.

Gillard is often off to the side, looking as un-starry and normal as anyone would photographed next to one of the world's most recognisable faces. The incongruity of the friendship between the prefect-like former prime minister from the Adelaide suburbs, and the doobie-smoking, Barbados-born RnB star is borne out in these pictures.

Does Gillard ever reflect on the enormity of the transition from Question Time with Tony Abbott to Malawi with Rihanna?

"I am eternally grateful for the fact that it's different - it's really rich and varied, what I do now," she says.

"It gives me experiences I would never have imagined, and it means meeting and dealing with someone like her. I'd never visited Africa before, and now I've been to lots of parts of Africa."

Another thing about the pictures of Gillard in Malawi: she looks uncomfortably hot, yes, and in the video where she's clapping along to Rihanna's singing, she looks as uncool and white - both literally and in the non-rhythmic sense - as possible. But she also looks undeniably happy.

Julia Gillard doesn't knit any more. She worries her needles will be confiscated in an airport somewhere and that she'll lose all her work.

During her prime ministership, she was a famous knitter. She knitted to unwind, having learnt the skill from her mother as a teenager. She knitted baby clothing for friends. She knitted a toy kangaroo for Prince William and the Duchess of Cambridge's firstborn, Prince George.

In mid-2013, when her government was polling badly, she was famously photographed for The Australian Women's Weekly with her knitting needles and the woollen kangaroo; Reuben the dog at her feet. The accompanying article detailed the discussions between the PM's office and the magazine over the nature of the article, discussions Gillard had assumed were off-the-record.

It was revealed that the idea for the shoot with the kangaroo had been cooked up by Gillard's media team. The whole thing was decried as another misstep. She was trying too hard to appear relatable. She was trying too hard to appear feminine. She was trying too hard.

In her memoir, Gillard recounts writing to The Australian Women's Weekly's editor at the time, Helen McCabe, to complain that she'd been treated "disrespectfully as a prime minister and shabbily as a human being" (McCabe later apologised).

The episode seems indicative of the ways Gillard tried to accommodate her femininity with her power, to integrate the two in a way voters could comprehend and accept.

During Gillard's prime ministership, Abbott famously stood at a volatile anti-carbon tax rally among signs calling her a "bitch" and "witch". Christopher Pyne on occasion compared her to Lady Macbeth and Madame Defarge, the knitting villainess from Dickens's A Tale of Two Cities, "who thought she was going to an execution and it turned out to be her own".

Does Gillard look back and wonder at the level of vitriol levelled against her as PM?

"Yes, I do still puzzle at it," she says.

"I think there were a lot of perfect-storm elements around it ... being first, the way I got there, and yes, it's the way so many others have got there ... [Also], ending up with a minority government.

"I mean, it was very easy for others to put the message out that 'she's not acting in the national interest, she's only acting in self-interest to keep her government alive'. The sort of living, breathing thing that the carbon tax, in inverted commas, became ... the hostility of sections of the media. I do, I do marvel at it. No, maybe not 'marvel'. 'Puzzle' is the right word. I puzzle at it still."

Gillard wrote about the famous 2012 misogyny speech in her memoir and has recounted the story of it countless times since, often for international audiences.

The circumstances that led to it - the disgrace of speaker Peter Slipper after his crude texts about women's genitalia were leaked - are now mostly forgotten. What is also forgotten is that Gillard was grieving when she gave it; her father, John, having recently passed away.

A month prior, broadcaster Alan Jones had told a Young Liberals dinner that Gillard's beloved dad had "died a few weeks ago of shame, to think he had a daughter who told lies every time she stood in parliament". Abbott condemned Jones's comments, but a month later, on October 9, stood in Parliament to move a motion to remove Slipper as speaker, and said that the government "should already have died of shame".

Afterwards, Gillard told The Monthly, "When [Abbott] used that word, 'shame', I did think, 'Now you've got it coming'. Yes, absolutely."

Most politicians have one or two moments that define them, and that speech, with the indignant rhetorical refusal in its opening line - "I will not" - has come to define Gillard. During her Sydney Town Hall talk, she told the crowd that "how I lived it is sort of different to what it's become". Asked if she resented being asked about it, she said she "used to", but "I'm more at peace with it now".

"The main analysis when I was prime minister was nothing that happened to me could be explained by gender, and if I ever said that, it was an illegitimate thing to say ... the woman-card argument," Gillard says today.

"Now there is a general acceptance that there is this thing called sexism in politics and we do have to think about it and we do have to try to eradicate it."

She agrees that the zeitgeist has caught up, and that things will be better for the second female prime minister.

"Women and men come up to me and say that they were so taken aback by it, they were sort of frozen into immobility and they're critical of themselves now for not having done more," Gillard tells me. "We're in an environment now where I think if any of those things happened again, the swarm of outrage would be enormous."

She thinks the media would be more considered, too. "I think many [editors] would say to themselves, in their heart of hearts, 'We are not going to do that again,' and they'd be more careful."

She wrote in her memoir that she "frequently felt let down" by women's organisations and groups that didn't "shine a light" on her treatment. In the same Town Hall talk, she said it would have helped if prominent male business leaders, too, had spoken up when sexist remarks were made about her.

In her memoir she ponders whether she should have called out her treatment sooner, but she "honestly" doesn't know if it would have made a difference.

I ask if she ever felt humiliated, or that she'd lost face following the abuse and her very public overthrow.

"Yeah," she says. "Your highest highs and your lowest lows are on public display."

I ask if that feeling of other people's eyes on her is part of the reason, for example, that she walked up to Tony Abbott in the Qantas Lounge at Melbourne airport in 2013, just after her ousting by Rudd, and shook his hand, to the surprise of onlookers; or why she's avoided poisonous commentary on her political enemies and their mistakes.

"I'd like to think people watch what I do and see dignity in how I've taken the defeat, but my strongest motivation is not to have constant toxicity and poison in my own head," she says.

"You know, I'm not going to sit in my lounge room, sharpening an axe for Tony Abbott. No, I'm not."

The audience for Gillard's Sydney Town Hall talk was testament to the power of her misogyny speech, the way it has soaked into Australian political history, and the current (seemingly unquenchable) thirst among women for hearing from female leaders.

The vocal, enthusiastic crowd comprised mostly women, split evenly between Millennials and the middle-aged. There was a peppering of men, including dignitaries from the University of NSW like Gillard's old education reform collaborator, David Gonski, its chancellor.

Gillard had just arrived from New York, and had a tale to tell about disembarking from the flight. As she did so, a hostess gave her a handwritten note from a fellow passenger.

"Dear Julia," it read. "You have done more than your share of emotional labour for our country already so I won't interrupt you..." The writer went on to say that she and her friends, when faced with a thorny problem, asked themselves "What Would Julia Do?" - or WWJD for short (Gillard later tweeted a picture of the note.)

The fangirling of the note, and Gillard's polished but genuine answering of questions on stage from SBS presenter Jenny Brockie, was incredible to watch. It seemed she'd become the heroine of every woman who'd ever copped a sexist comment and was too indignant or flummoxed to respond adequately, but who later had what the French call esprit d'escalier, imagining the perfect comeback, but too late.

With her misogyny speech, Gillard had acted out a revenge fantasy, or a justice fantasy, that was so universal it made many women feel like she was theirs, somehow. That must be a pretty big upside to having been the first female PM.

"I was brought up in the reverse of a combative environment," Gillard says now. "But I was brought up to stand my ground debating, and I never wanted the impression to settle that women can't or shouldn't do this, that the nation can look at Paul Keating delivering a withering one-liner and say 'That's fantastic', and look at a woman commanding the same adversarial space and be critical of her.

"I didn't win every day but I do think I had that skill set, that I could command that space. The misogyny speech is the most noted of those, but it's not the only time."

At one point during our interview, I ask after Gillard's mother Moira, who I learn died a couple of years ago.

"There's a reason you don't know, which is, we kept it very quiet," she says. "We didn't want to go through, I mean, we weren't publicly exposed at that point, as when Dad died. But we didn't want to run any risks and make any announcements or statements about it."

Gillard's father once said, "When I'm with Julia, I walk six inches taller." He was intimately involved in her career. He followed every political development closely and read the press diligently.

Her mother, on the other hand, focused mostly on filling her in on family news - or would call after watching Question Time to tell her she looked tired.

Politicians are humanised by their families. That's why we see so much of their adoring wives and pretty children during election campaigns. But Gillard was no one's mother and no one's spouse. As a nation, we seemed to collectively forget that she was someone's daughter.

Gillard gets asked a lot about resilience. She believes it's a muscle which must be exercised, and says she's actively cultivated it. She believes in a moderate approach to all things and in "being a bit reflective about your own thoughts and feelings, where you are and why you're there, and working through how you can get to a better place".

"I think instinctively I've done that all my life," she says. She refers to the CEO of Beyond Blue, Georgie Harman: "Georgie says it's a roof over your head, it's a purpose in life, and it's a date on Saturday night."

Did she ever fall apart behind closed doors? "No, there was never a moment when I was weeping in my bed, throwing crockery around. Nothing like that. I mean, there were moments when you ... I felt the weight of it. I don't want to give the impression I was somehow impervious ... [but] I was pretty disciplined about not letting too much of the muck get inside my head and really weigh on me. But even with that, some of it does."

I ask why she thinks she's managed to transition well from politics. She credits that discipline, plus a quick exit - she made her last parliamentary appearance soon after she lost the leadership in late June 2013, months before the September 2013 election in which Tony Abbott beat her replacement, Kevin Rudd.

"I called the last leadership ballot on the basis 'winner stays, loser goes', and you know, I think I picked the right moment to exit politics. Not everybody does," she says.

"I have been very thoughtful and, I hope, disciplined about not taking the hurt with me, certainly not taking bitterness with me. You know, my political career was a handful of aces. To be in government, to be deputy prime minister, to be prime minister. I wanted to take the good with me and let go of the not-so-good.

"I've been disciplined about that, and I've been part planned and part lucky about the opportunities that have come my way since."