The general belief about Wollongong is that it does things its own way. It's fiercely independent, a little bit bolshie, always up for a good time and massively under-rated. Myth, or reality? I have no idea, but Babyface is all of the above and more.

The restaurant recently turned five years old so I thought I'd give them a present – a review in the hallowed pages of Good Food. Happy birthday!

Right in the middle of The Gong, Babyface has the attitude of a lo-fi wine bar with a serious kitchen at its heart. The effect on first walking in is of concrete and brutal minimalism, with a long bar down one side and wood-topped tables and banquette the other.

Keep going and you reach a short flight of stairs that go straight into an open kitchen where head chef Andy Burns and his team do their thing. (If you're going to the loo, turn a quick right instead, unless you want to be put to work.)

Burns opened Babyface Kitchen in 2016 with Gen Digregorio and Gavin Tidbury as a sort of contemporary Japanese robata-fuelled restaurant.

Over time, they've dug deeper into smoke, fire and barbecue, and now Tidbury runs the other half of the business, Two Smoking Barrels barbecue joint and food truck.

I'm in for Saturday night's seven-course set menu, which kicks off with a snack attack of crisp little chickpea pancakes topped with spanner crab and oyster emulsion; terrific pasteis de nata tart bases filled with house-made boudin noir and a fruity, lacto-fermented tomato sauce, and little discs of pressed cucumber with cream and green ants.

More pastry is on the way – malawach, a flaky, laminated Yemenite pastry that's spiralled and pressed into the pan like a Chinese spring onion pancake, ready to scoop through house-made buttermilk ricotta and brown trout roe. Then a plump, grilled chicken wing stuffed with duck leg and pine mushrooms, under a fermented honey glaze.

There's good energy in the room, with lots of tables for twos talking wine, and a long table coming in for a celebration. Digregorio's drinks list is equally lively, running to spritzy cocktails, craft beers, and a meaningful, well-priced list of natural, small-producer wines. An egalitarian 2020 Gentle Folk Village pinot noir ($80) from the Adelaide Hills is quite happy crossing from seafood to poultry to meat.

Fish is taken seriously here, with renowned supplier Costa Nemitsas sending line-caught, ike jime-spiked fish from Australia's top fishing folk. Tonight, however, it's a crisply seared fillet of Murray cod – our best farmed fish – on a buttery pil pil sauce of emulsified fish juices, next to a chop-chop of sugarloaf cabbage, zucchini and hazelnuts.

Service from Digregorio and Jonathan Penny is intuitive, letting you know what you're eating without droning on. I also like how some courses are shared from the one dish and others, like the wagyu beef, are individual.

A single, ruby-pink finger of seared Ranger's Valley wagyu rib cap is rested, relaxed, and oozing with fatty goodness. Just in case there isn't enough richness, there's also a crisp, golden brick of wagyu-fat hash brown, salt-baked celeriac, shiitake and thyme sauce and an intensely sweet, blackened carrot cooked over charcoal.

It's all very rich and filling, but somehow I'm not struggling. Not until two desserts arrive, that is: a creamy/crisp dacquoise, and charred pineapple with sweet blackberries, granular chocolate soil and an almost savoury roasted kombu ice-cream. If I finish them, they'll have to send in the forklift.

It's not an easy dining experience to describe, with some old ideas – charred carrot, compressed cucumber, bread served halfway through – and some new, like malawach. But the DNA is strong, with distinct, satisfying, wine-friendly flavours from direct cooking methods such as grilling and charring, and recurring themes of smoke, umami, butter and pastry.

So yes, Babyface IS a bit different. Whether that's a Wollongong thing or not doesn't actually matter; it's just a good thing.

The low-down

Babyface Kitchen

Drinks: Good value to be had on the small-producer wine list and an interesting wine/drinks pairing for $70.

Vegetarian: Several a la carte options, or give 24 hours notice for vegetarian and vegan set menus.

Pro tip: The Babyface cocktail is zingy with yuzushu, gin, lime and tonic, $19.