It was at around 3am on a Saturday morning that I realised Isted Grill, a Danish/Chinese fast food shop in the heart of the happening Vesterbro district, was on to something. I’d been dragged back there by my vegan friend – who earlier that evening had suffered a total collapse of principles the moment his nose picked up the scent of sizzling roast pork – and we were queuing for a second round of its famed flæskesteg sandwich.

This long-running, late-night snack joint has gained a city-wide reputation during its 30-odd years, and its classic Danish pork rolls are things of beauty. A slice of roast pork with crackling is heated on the grill before being tucked inside a soft white bread bun, topped with braised red cabbage, pickled cucumbers and a touch of mayonnaise.

Facebook Twitter Pinterest Photograph: Jack Lee

Something that delicious is probably best described in cliches, so, here goes – it’s like a party in your mouth. Or maybe a flavour explosion. Either way, it begins the moment your teeth crunch through the salty, fatty crackling.

The bland, white tiled shop itself has, I’m told, hardly changed since it opened in the 1980s, and it’s still run by the same husband-and-wife team – Mr and Mrs Lee. The sandwiches cost less than £3, so the prices seem to be frozen in time too. Perhaps that explains why the shop was full of tall, drunk Danes when we arrived for our first evening snack, and was still full of them when we parked our bicycles outside for our second. Isted Grill’s flæskesteg sandwiches are probably the best thing you’ll eat in Copenhagen – as my vegan friend will confirm.

• Isted Grill, Istedgade 92, istedgrill.dk