Restaurant 1701, Bevis Marks Synagogue, London

You could eat in the sleek grey room and not realise it was a Jewish restaurant

Well, this is awkward. I've arranged to meet David Baddiel at Restaurant 1701, a smart new kosher restaurant in the grounds of Britain's oldest synagogue, but I'm having trouble finding it. David has phoned me to say he has arrived, and "it's much more Jewish than I was expecting".

I finally find the place, beyond the Bevis Marks synagogue, in a security-gated courtyard. And it's completely empty. I call David. He's a few streets away, in another kosher restaurant – also called Bevis Marks – where he's ordered a drink, eaten a piece of bread and counted at least three women wearing sheitels.

When David eventually joins me, in a kosher-salted sweat, he announces "I am now officially the wandering Jew". The staff handle our farce with cordial politesse, but the silent, formal room, in which we remain the only diners, makes David nostalgic for his abandoned lunch spot. It may not have offered the ambitious, genre-bending menu of 1701, but at least it had customers.

Then the food starts coming, and we realise why we're here. Restaurant 1701, which is backed by the kosher food group Adafina, belongs to what might be called the Ottolenghi diaspora, if that didn't seem an inappropriately frivolous usage in this context. Head chef Oren Goldfeld comes from Israel by way of Yotam Ottolenghi's Nopi. His cooking here may be restricted by the laws of kashrut, but it is remarkably adventurous, drawing on the Middle Eastern and Iberian influences of the Sephardi tradition, as well as the pot-sticking Ashkenazi comfort food of Eastern Europe.

There are familiar-sounding dishes on the menu, of the chopped liver, chicken soup and gefilte fish persuasion, but they are a world away from the lumpen versions in most Jewish restaurants. Chopped liver arrives as an airy-textured mousse holding crisp shards of chicken skin, and fancily accessorised with a foie gras foam, peeled grapes and a rubble of crumbled gingerbread.

Another starter, pastilla, a miniature version of the sweetened meat and fruit pie from Morocco, is simply one of the most delicious things I've ever tasted; crisp filo pastry enfolding a dark braise of spiced lamb neck, and a just-sweet-enough syrup of spiced fruit and nuts. And that chicken soup is so good, we can almost forgive its billing as 'Jewish Penicillin'. Clarified to an amber purity, its flavour concentrated and refined, it holds firm meat-filled tortellini in place of matzo balls. "It's almost too nice," David says. "Where's the schmaltz?"

His unhappy memories of the kosher food he endured at school – the dairy-free custard coloured bright blue to make it more appealing – are definitively banished by a main course of flanken, traditionally boiled beef ribs served with horseradish. Here the short ribs have been smoked in hay, then cooked low and slow, to leave the meat glossy and almost black, the smoky-sweet flavour brilliantly underscored by celeriac purée and a sticky pomegranate jus (non-wandering).

There's a certain fine-dining flourish to the presentation – all those dots and dashes, foams and rubbles – which won't be to everyone's taste; as David says, "I don't associate this kind of daintiness with Jewish cooking. It's all about eating huge portions of starchy food, then going back into hiding". But it's done with such assurance and care, and the flavours, if not the portions, are reassuringly huge.

Under kosher rules, meat and dairy can't be prepared or eaten together, but I don't register the absence of dairy until David quizzes our waiter about coffee and is offered a soya cappuccino. Puddings arguably suffer; a sturdy orange-blossom-soaked semolina cake, tishpishti, comes with on-trend trimmings – carrot sorbet and a dehydrated black olive 'soil' – when what it really needs is a nice bit of cream. And a Frucht Zup, a posh fruit salad anointed with a strawberry and black pepper consommé, reminds David of the gimmickry of his feared blue custard.

Service is informed and unobtrusive (harder than it sounds, with only two customers) and the kosher discipline is lightly worn; you could eat in this sleek grey room and not realise it was a Jewish restaurant. Prices, though, are high, presumably reflecting the extra care that goes into sourcing and preparation. Mains range from £17-£30, and we paid about £80 a head, including service and a glass of Barkan Pinotage (kosher, of course).

It's unexpected, but rather delightful, to find ancient dietary laws producing not limitation, but open-minded, adventurous cuisine. Traditionalists looking for faithful reproductions of heritage dishes might be disappointed. But Restaurant 1701 deserves to be sought out by the foodish, as well as the Jewish. Just check the address first.

Food ****
Ambience **
Service ****

Restaurant 1701, Bevis Marks Synagogue, Bevis Marks, London EC3 (020-7621 1701). About £160 for two with a glass of wine