Slice the beef on an electric meat slicer, or use the following method: with plastic wrap, tightly roll the steak into a torpedo or log shape. Put the beef in the freezer for 30 to 45 minutes to firm it until tight but not frozen. Remove the plastic wrap and, working quickly; use an electric knife to slice the beef into paper-thin slices, almost shaving the beef. If this does not produce very thin results, cut the beef into the thinnest slices possible and flatten, using a meat pounder. Once all the beef has been cut, refrigerate until the remaining ingredients are ready.

Heat 2 tablespoons of the oil in a heavy-bottomed saute pan set over low heat. Put in the onions, season with salt and pepper, and cook until nicely softened and lightly caramelized but not browned, about 20 minutes. Transfer the onions to a bowl and set aside. Add the pepper halves to the pan, season with salt and pepper, and fry until soft and tender, about 12 minutes. Transfer to the bowl with the onions. Keep the onions and peppers covered and warm.

In a clean, heavy-bottomed saute pan, heat the remaining oil over medium heat. Add the beef in batches and lightly brown, seasoning with salt and pepper as you cook, adding more oil if necessary.

Pull out a little of the doughy insides of each loaf, then drizzle lightly with the oil, a splash of vinegar, and a pinch of salt and pepper. Put 1/4 of the beef inside each roll, top with onions and peppers, and finish with several slices of cheese. Cover with the top half of the bread. Wrap snugly in sandwich wrapping paper, slice diagonally in half, and serve.