Preheat your oven to 400 F. Arrange the peppers cut-side up in a large baking dish. 

Heat the oil in a large skillet over medium-high heat. Add the mushrooms and cook 3-5 minutes, until deeply browned. Add the onions and cook until golden brown.

Transfer the mushrooms and onions to a plate and return the skillet to the stove. Add the steak and season with salt and pepper. Cook 2-3 minutes per side, until browned. Stir the peppers and onions into the steak.

Place one slice of cheese inside each pepper. Top with the steak mixture and another slice of cheese. 

Bake for 25-30 minutes, until the peppers are soft and the cheese is melted and gooey.