In a large bowl, combine bell pepper, onion, garlic, mushrooms, and ham. Mix well. In a smaller bowl, whisk together eggs, heavy cream, salt, and pepper. Add whisked eggs to vegetable bowl and stir. Incorporate potatoes, then 1 cup of shredded cheese. Pour casserole mixture into an 8x8-inch greased baking dish. Sprinkle remaining cheese over top. Bake at 350 degrees for 30–45 minutes, until cooked through and eggs are set. If using a broiler-safe dish, turn on broiler for 2–3 minutes to crisp and brown cheese.