Ox Club, 19a The Headrow, Leeds LS1 6PU (07470 359961). Meal for two, including drinks and service: £80

Stacked up in front of the white tiled bar at Ox Club in Leeds are brown paper sacks of “British Barbecue Charcoal” alongside piles of kindling, both provided by the Leeds Coppice Workers. It’s a co-operative that manages woodland and sells the resulting kindling and logs. Three decades after I finished my degree in Leeds, the existence of the company makes my heart twang with nostalgia. Leeds is a big-boned city, full of Victorian heft; in the 80s the details of glowering façades were picked out in diesel grime. But even so you always felt the rugged presence of the countryside to the north, of the rocky outcropped hills and the clefted valleys. The existence of Leeds Coppice Workers suggests that the dialogue between town and country continues. As does this restaurant. The self-conscious log pile threatens us with rustic beardy parody. The cooking dodges all that.

Leeds is a cleaner place now. The students may always have been vital to the pub economy, but back then there were some saloon bars you did not dare enter; establishments like the Whip, where the glass collectors swept up the shattered tumblers and called the ambulances. Ox Club occupies one of those yards, set back from a main drag. It used to be home to a drinking den named Big Lil’s. Now Lil has gone and the building houses a buffed up events space, a beer hall offering dozens of ales and this restaurant. It’s the second project from the team behind the Belgrave Music Hall, including chef Ben Davy.

‘You end up with forkfuls of soft fried egg white and crunchy vegetables’: duck egg with girolles. Photograph: Alex Telfer/The Observer

At Belgrave, Davy did street food including the obligatory burger. At Ox Club he is putting aside rudimentary things. It is his grown-up restaurant, complete with a fancy Grillworks grill imported from Michigan. Starters are around £7, with mains in the teens. The challenge for a restaurant with a particular shtick, like a solid-fuel grill, is to avoid becoming hostage to it. The menu flashes warnings on this front, as if in the open kitchen it is all guttering flame and heat and sweat. There are references to burnt banana leaves and burnt leek hearts. There’s charred corn, charred pineapple and charred cabbage. Everything else may or may not be smoked, including the cooks.

The genius dish is the cubes of melon with fermented chilli. It’s one of those ideas you want to pass off as your own

The reality is more nuanced. It begins with a bowl of liquid golden chicken schmaltz and cubes of bread to dredge through it. There may have been a saucer of olive oil and balsamic somewhere on the table, too, but really, who cares when you have rendered chicken fat to play with? The surface is dusted with flakes of salt that haven’t yet quite dissolved. You are being given the licence to do at the table what you do in the kitchen when you are sure no one else is looking. Or am I the only one who drags bread through the bottom of the roast chicken pan when it’s finished with?

The cooking here is boisterous and assertive. It’s determined to make a point. A fried duck egg is pelted with girolles that have been sautéed to crisp alongside fried up leaves of lightly bitter cavolo nero, that have the edge of that stuff Chinese restaurants flog as deep fried seaweed. There are fronds of mustard leaf, and the whole is brought together by drifts of finely grated pecorino. The yolk leaks. You end up with forkfuls of soft fried egg white, and crunchy vegetables, and salty cheese. On another plate three densely textured fillets of smoked eel are softened by a smooth pea purée lifted from overt, buxom sweetness by the addition of a little miso. But the genius dish, the one that cleans the palate, is the cubes of melon with savoury fermented chilli. It’s one of those ideas you want to steal and pass off as your own. Oh sure, I’ve been mixing melon with fermented chilli for yonks. Haven’t you?

‘Lifted from overt, buxom sweetness by a little miso’: smoked eel and pea purée. Photograph: Alex Telfer/The Observer

The grill kicks in with the mains. A piece of trout, with silvery, heat-blistered skin like crackling, sits on a thick creamy sauce spun through with smoked roe. It’s the essence of cod’s roe on toast. Alongside the fish rises an island of knotted leek hearts, blackened and crisped at their edges, a mixture of sweet caramelised onion and something altogether more astringent and interesting. A side dish brings two pieces of corn on the cob, roasted over the wood then smeared with a butter made with black garlic, which is funky and earthy and deep. The shared cooking method leaves everything with the light tang of bombfire. A little goes a long way, but here it’s suitably controlled.

A piece of guinea fowl roasted on the bone comes on what they describe as a “cassoulet”. It isn’t, in any way; it’s a white bean stew, with a few vegetables playing supporting roles. But it’s no less comforting for all that. It’s scattered with “Yorkshire pecorino”, a phrase calculated to bring the Italian community to the gates with pitchforks and burning stakes. Forget provenance; it seasons the dish perfectly. It’s the details that count here. A side of spinach leaves with an anchovy dressing and a crumb of toasted rye bread for texture seals the deal by the addition of a tiny amount of granulated sugar.

‘It’s the details that count’: a side of spinach leaves with anchovy dressing. Photograph: Alex Telfer/The Observer

Desserts don’t quite match up to the savoury courses. A pudding of black rice is topped by a pandan leaf ice-cream, which was a mystery to me when I read about it and remains so after I’ve eaten it. The ice cream has a slightly fruity edge. I can say no more. A big rice cracker, like a poppadum laid across the top, is a cute touch, but none of it is quite sweet or compelling enough. No matter. There’s a toasted piece of brioche spread with strawberry jam then crusted with sesame seeds, crushed peanuts and a few other things. Finally it’s topped with a peanut butter ice cream. That’s plenty sweet enough. As a take on the peanut butter and jam sandwich it works, though with little subtlety.

But who cares? By which I mean, what about that chicken schmaltz right at the start? Because I’m not going to let a ho-hum dessert or two get in the way of a bit of fandom. Ox Club has, in its genes, the potential to be seriously bloody annoying; the solid fuel mission statement is a poseur’s charter. But they know what they’re doing, and they’re doing it at a reasonable price too. This corner of rustic country cookery in the heart of the city more than works.

Jay’s news bites

Neil Rankin’s two Tempers, in Soho and the City of London, put burning wood front and centre. Whole animals (or for beef, large parts thereof) come into the restaurant, are broken down into their prime cuts and grilled. In Soho there’s a Mexican take, with tacos; in the City it’s Indian spicing. Either way it’s brilliant theatre and you leave with the smell of smoke in your hair (temperrestaurant.com).

Tim Thornton and Trystan Ross-Williams met on the jazz course at the Birmingham Conservatoire. While Tim continued as a bassist, Trystan became a cook and then senior sous chef at Angela Hartnett’s Murano. Now they are coming back together for Karve, a pop-up involving three ‘sets’ of dishes with live jazz. The first event will take place at the Pill Box Kitchen in London’s Bethnal Green on 11 November. (karvefood.com).

We may as well celebrate the upside of a low exchange rate, courtesy of Brexit. British beer exports are booming, with the billionth UK-brewed pint recently shipped abroad. The business is now worth £600m a year.

Email Jay at jay.rayner@observer.co.uk or follow him on Twitter @jayrayner1