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Heat the oil in a heavy-based pan or casserole dish set over a medium heat. Add the onion and peppers along with a good pinch of salt and fry for 20 mins, or until the onions are golden and sticky. Add the vinegar and cook for a further 5 mins. Season to taste.
Using a sharp knife, slice the steak as thinly as possible and pile the slices into four portions. Heat a skillet over a high heat until almost smoking. Put one portion of the steak slices in the pan in a pile that's roughly the length of your rolls. Fry for 3 mins over a high heat until some of the steak is cooked through, with pink bits remaining. Pile a quarter of the onion mixture on top, as well as a quarter each of the cheese slices and the mozzarella. Continue to cook undisturbed over a medium heat for 5-10 mins until the meat is brown and crisp around the edge and the cheeses have melted. Split one of the rolls open and carefully scoop the meat and cheese mixture into it. Repeat with the remaining meat, onions, cheese and rolls.