Is there a more iconic brunch sight than an oozing yolk, a lazy spill of golden eggy sunshine? I think not. And yet, at Small Axe, a six-year-old cafe in Brunswick, they nevertheless manage to elevate an icon into something approaching true godliness: their egg flows not over mere toast but onto pasta, in the process creating one of Melbourne's most beautiful and beloved brunches.

Small Axe's breakfast pasta is the upshot when bacon and eggs on toast take a trip from Melbourne to southern Italy and back again. Maccaruni – a slinky twist of pasta – stands in for toast. It's tossed with crisped guanciale (cured pork jowl, subbing for bacon), peas and mint, then topped with salted ricotta and a slow-cooked egg.

The diner destroys the egg, prompting the yellow lava flow, then tumbles the elements to create a sticky mess of carbs and salted pig. Simple indeed and sublime for sure.

The pasta speaks to Small Axe's mission of bringing a taste of Sicily to Brunswick's brunch array. Chef Adam Pruckner's mother was born in Sicily; together with his event manager wife Kirstyn Tate, they've distilled dishes, ingredients and the culinary philosophy of Italy's rugged, resonant southern island and seamlessly woven them into a very Melbourne cafe experience.

Some dishes are explicitly Italian – the pork and veal meatballs have pine nuts and sultanas, just as Adam's nonna made them, and the mozzarella in carrozza is the kind of deep-fried cheese sandwich you can get on the streets of Palermo – but others are more subtle.

The hot dog stars a housemade Italian-style pork-and-fennel sausage; along with provolone cheese and chef's own red pepper relish, it's stuffed into a brioche bun as a kind of hat-tip to the Italian predilection of sweet pastries for breakfast.

The French toast offers an approving nod to the Euro cake-in-the-morning approach while also expressing the peasant parsimony of the Sicilian kitchen. Bread crusts are saved and turned into a bread-and-butter pudding loaf that's then sliced, egged and fried to form the golden, crisp base for a Sangiovese-poached pear. It's a wholly enjoyable mash-up of luxury and frugality.

Smoked eggplant salad leans into the Arabic ingredients that invasion and occupation threaded through Sicily – the smokiness, almond hummus and pomegranate are big on flavour as well as a gentle history lesson.

Small Axe Kitchen looks small from the street front with its window perches and busy counter, but it goes a long way back and also has a dog-friendly side terrace with plenty of blankets for laying over winter-chilly laps.

Rather than drawing customers because it's new or trendy, this busy, confident cafe keeps people coming back because it's friendly, reliable, fanatical about quality and has a strong sense of identity.

How lovely it is to be somewhere that knows who it is and has worked out how to express it – and has an iconic egg dish to boot.