Preheat the oven to 350°F. Heat the butter in a large ovenproof skillet over mediumheat. Add the onion and garlic. Cook until the onion is translucent and the garlic is fragrant.
Add the mushrooms and peppers to the skillet. Cook until the mushrooms release their liquid and the peppers are crisp-tender, about 10 minutes.
Add the roast beef to the skillet and mix with the vegetables. Taste, and add salt and pepper, if desired.
Top with the provolone cheese, then sprinkle the mozzarella cheese over the top in a nice, even layer.
Bake for 15 minutes, then finish under the broiler for 2 to 3 minutes, until the cheese is browned and bubbling.