“It’s going above and behind the regular service,” said Alexander Hall, who opened Brunswick in Bedford-Stuyvesant, Brooklyn, earlier this year. He plans to have 12 Brunswick locations in New York by 2016. “There are so many cafes in Melbourne, and the standard of coffee is so high, and the design is so high, the only way to differentiate yourself is with customer service.”

The accent helps. “You kind of go along with it, because believe it or not it’s still a novelty in this country,” said Mr. Hall, who tends to hire Australians on visas that allow them to work in the United States. “These young girls and guys are upbeat people, traveling around the world, having a good time. It’s breakfast. It’s not serious; it’s meant to be fun.”

Each cafe has a distinct personality: Bluestone Lane, in Greenwich Village, is stylish and relaxed, with the whitewashed walls and hanging planters of a tasteful beach house; Brunswick has the clean lines and clever light fixtures of a design store. But they all have one thing in common: the avocado smash.

Sometimes called an avocado toast (and in the United States often associated with California), it’s comfort food for any time of the day. You smash half a ripe avocado onto a thick piece of multigrain toast, season it with salt, pepper and chile flakes, then give it a splash of olive oil and a squeeze of lemon. Anything else is a flourish: dukkah (an Egyptian spice mix), toasted pumpkin seeds, a poached egg.

Image Bluestone Lane's morning salad with smoked salmon. Credit... Fred R. Conrad/The New York Times

In Australia, cafes play a central role in a certain kind of lifestyle you find near the beach. “You wake up, go down to the beach, have a swim, then go have some coffee and poached eggs and toast,” said Henry Roberts, an owner of Two Hands.