Slice the stack of roast beef very thinly across the grain, and then chop once or twice across the strips.
Heat 1 tablespoon of the oil in a large skillet (12 to 14-inch diameter) over medium-high heat. Add the roast beef and toss with a spatula, separating any chunks as you go. Add a few dashes of Worcestershire sauce and cook only until warm, about a minute or two. Remove to a plate.
Add the second tablespoon of oil to the same skillet. Then add the onions and peppers and cook, stirring regularly, until the veggies are tender with some golden brown edges, about 7-8 minutes. Add a sprinkle of salt and pepper while sautéing.
To build the sandwiches, place equal portions of the roast beef on the bottom half of each roll. Top with the onions and peppers, and then spoon the cheese sauce over all. After topping with the other half of the roll, you may wish to secure with two toothpicks and then cut the cheesesteaks in half.