He has always seemed happy for his memorable performance as mob consigliere Silvio in The Sopranos to remain a one-hit wonder – his first and last unforgettable acting role. But that all changed when Steven van Zandt got a call from Norwegian TV. Now we have Lilyhammer, currently midway through its run on BBC4, in which Van Zandt plays New York mobster Frank "The Fixer" Tagliano, who rats out his crime-family boss after surviving an assassination attempt. As the title suggests, he then moves to Lillehammer under a witness-protection programme – becoming Giovanni "Johnny" Henriksen and building a new life far from the vengeful hoods who want him dead.

Much as I loved Silvio I've found Lilyhammer a tough show to care about. Maybe I've been spoiled by those other Scandinavian imports Forbrydelsen, Borgen and The Bridge, all of which share a complexity and sophistication that demand full attention, stand up to repeated viewings and leave you buzzing for the next episode. Lilyhammer, on the other hand, leaves you much as it found you. Van Zandt's performance is as broad as one might expect: he doesn't so much act as do his Silvio thing. It's a mobster caricature, how you'd dress and act at a gangsters and molls party. There's nothing in the world wrong with that, just don't expect too many layers from him.

Tonally, Lilyhammer is an odd show. The fish-out-of-water mobster bumping up against the safety-first bureaucratic nightmare of Norway feels very ITV Sunday night – and yet they have no problem throwing in the odd "motherfucker" (helpfully adding to the Scandinavian profanisaurus kicked off by Jan Meyer's "For helvede Lund!" in The Killing). It's Heartbeat with snowboots and swearwords.

It's also a feature of the show that everything falls into Johnny's lap with the minimum of effort. Just four episodes in and he's already a bar owner, property developer and father (twice). I know he's Frank the Fixer but the writers here put less effort into solving problems than they did on Entourage. It's obviously an effort for Van Zandt to uproot to another continent, but Norway seems a long way to go to make a show that could have easily been made closer to home. Northern Exposure, which surely must be an influence, covered a lot of the same ground without leaving the US.

Over on the right side of the law we see quite a nice mother-son relationship between chief of police, Laila, and her assistant, Geir. One of Norway's lesser Elvis impersonators, Geir may be a colossal idiot but there is something endearing about him – the brief friendship he has with a Sikh he ineptly racially profiles was one of the funnier moments from last night's show. Geir at least realises that there's something not right about Giovanni Henriksen even if he's a bit sketchy on the details.

Given how slapdash law enforcement is with Johnny's records, it can't, in any case, be long before his New York enemies locate him. And it's not like he's keeping a low profile. He's cracking heads, making deals, using a child to intimidate some harmless old hippie out of his home – it's like he never left New York. The refrain on Boardwalk Empire is: "You can't be half a gangster." So where does that leave Johnny? Is he in or out?

I can't speak for him, but I think I'm out. Johnny may be impressed by the clean air, fresh white snow and gorgeous broads but Lilyhammer leaves me cold. How are you finding it? Bada-bing or fuggedaboutit? Let us know below.