Place steak in freezer for 30 to 45 minutes; this makes it easier to slice the meat. Remove the meat from the freezer and slice very thinly.
Heat griddle or grill pan over high heat. Brush steak slices with oil and season with salt and pepper. Cook for 45 to 60 seconds per side.
Place several slices of the meat on the bottom half of the roll, spoon some of the cheese sauce over the meat, and top with the mushrooms, onions, and peppers.
Melt butter in a medium saucepan over medium heat. Whisk in the flour and cook for 1 minute. Slowly whisk in the warm milk, and cook, whisking constantly until thickened, about 4 to 5 minutes. Remove the mixture from the heat and whisk in the provolone and Parmesan until combined; season with the salt and pepper.
Heat butter and oil in a large saute pan over medium heat. Add the onions, season with salt and pepper, and cook slowly until golden brown and caramelized, stirring occasionally, approximately 30 to 40 minutes.
Heat oil and butter in a large saute pan over high heat. Add the mushrooms and cook until the mushrooms are golden brown. Stir in the parsley and season with salt and pepper.
Heat the oil in medium saute pan over high heat. Add the peppers and cook until soft. Season with salt and pepper.