They have been steamed, fried and kept warm in bain-maries for nearly 70 years.
And now a Melbourne culinary icon could be cooked up in bronze, if a campaign to build a lasting tribute to the dim sim succeeds.
A group of RMIT students have launched a petition calling for Melbourne lord mayor Robert Doyle to build a statue to "honour this piping hot beacon of our all-inclusive culture".
"In Melbourne we're quite quick to name streets after famous people and build monuments to footballers and I think we've forgotten our cultural heritage," Dim Sim Salute co-founder Dan Lewry told Fairfax Media.
"We are the food and cultural capital of Australia so we need to honour something that introduced Australia to Chinese food, and that's the dim sim."
William Wing Young is believed to have first concocted the modern dim sim at his restaurant in Melbourne's Chinatown in 1945.
His creation - a larger and thicker-skinned version of a Chinese dumpling - has since become a staple in fast-food stores across the country.
While inspired by the Big Banana in Coffs Harbour and Woombye's Big Pineapple, the Dim Sim Salute has proposed something more subtle.
"We'd preferably like to see a bronze statute, none of these huge fiberglass things, just something small and humble," he said.
The mayor minced the idea on Wednesday however, telling radio station 3AW he had to stick with tradition.
"I don't think that there's any doubt that there's a replacement for the meat pie and we already have the most magnificent memorial to that standing right in the middle of the showgrounds [the 'Pie in the Sky' at the Royal Melbourne Showgrounds]," he said.
"I respect the passion of these people but I really can't see this one going anywhere."
I am a traditionalist: the meat pie trumps the dim sim in this town. And rightly has a monument. @RossAndJohn pic.twitter.com/qdFtfv2Q0l — Robert Doyle (@LordMayorMelb) September 2, 2014
Mr Lewry said they would consider negotiating with other councils if they could not convince the City of Melbourne to support the idea.
He said it had not yet been decided which version of the dim sim the proposed statute should honour: fried or steamed.