Slice the tops off the bell peppers, remove seeds and ribs, and thinly slice them. Set aside.
In a large, deep ovenproof skillet or Dutch oven, melt the butter over medium heat. Add the onion and garlic and sauté until the onion turns translucent and the garlic is fragrant, about 7 minutes.
Add the sliced mushrooms and bell peppers to the pan. Cook for about 10 minutes, until the mushrooms release their moisture and the peppers become slightly tender.
Preheat your oven to 350°F.
Mix the roast beef into the skillet with the veggies. Taste the mixture, and season with salt and pepper if desired. Layer the provolone cheese over the top, followed by the shredded mozzarella.
Bake for 15 minutes, then switch to broil for an additional 2 to 3 minutes until the cheese is bubbly and golden.