Preheat oven to 375 degrees. Line a sheet pan or 9 x13-inch baking dish with foil.
Heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet, over medium high-heat. Sauté green peppers and onions, season with salt and pepper to taste. Cook until the onions are translucent and the peppers are soft. Remove the vegetables to a bowl, loosely cover with foil and set aside.
Add 1 tablespoon olive oil and 1 tablespoon butter to the skillet. Working in batches, add half of the thinly sliced steak, cook until brown, turning frequently. Sprinkle with Montreal steak seasoning to taste. Stir in 1 tablespoon Worcestershire sauce while the beef is browning. Remove to a bowl, loosely cover with foil and set aside. Repeat steps with remaining steak.
Slice the buns in half at once, keeping them all together. Place the bottom buns in the prepared baking sheet facing up. Spread 1 1/2 tablespoons mayonnaise over the bottom buns. Top with 4 slices of cheese. Arrange steak, peppers and onions over the cheese. Top with 4 more slices of cheese. Spread 1 1/2 tablespoons of mayonnaise over the top buns and place them on top. Pour 1/4 cup melted butter over all and sprinkle with Parmesan cheese. Cover with foil and bake for 15-20 minutes until the cheese is melted. Unwrap and devour!
Cook's Note: Place steak in freezer for 30 to 45 minutes; this makes it easier to slice the meat very thinly.