Preheat the oven to 350 degrees. Slice the tops off the peppers and hollow out the inside. Place the peppers on a greased baking sheet, hollow side up, for 15 minutes. While they bake, prepare the rest of the meal.
Take the tops of the bell peppers and slice the remains into thin strips.
Heat the olive oil and butter in a medium skillet over medium-high heat. Add the onions, sliced pepper tops, and mushrooms and sauté for about 5-7 minutes, until the onions have softened.
Add the shaved steak and desired amounts of salt and pepper. Sauté until all sides of the steak are browned. Use a spatula to toss it around occasionally. This takes about 10 minutes or so. Drain excess liquid from the pan.
Add the cheese to the pan, toss around slightly, and cover the pot. Turn off the heat.
Remove the peppers from the oven and use an oven glove to pour out any liquid within the middle of the pepper.
Use tongs to fill each bell pepper with that delicious filling, and serve!