Butter a 9x13 casserole dish. Place buns cut side down to cover the bottom of the casserole dish, filling in empty spots with broken pieces of bread. Top with ham and diced red pepper.
Mix together eggs, milk, dry mustard, pepper, onion and chopped pepper. Pour mixture on top of buns. Sprinkle with 2 cups cheese. Cover with plastic wrap and refrigerate overnight.
In the morning, preheat oven to 350F. Sprinkle casserole with remaining cheese.
Melt butter and mix with breadcrumbs. Sprinkle over casserole. Bake uncovered for 60 minutes. Check after 45 minutes. If the top is getting really browned, loosely place foil for remainder of cook time.
Once done, remove from the oven and let rest for 10 minutes before serving. The breakfast casserole puffs up while baking, and settles after it's been out of the oven for a few minutes.
If you prefer less crumbs, pour ¼ cup melted butter over top of casserole, mix ¼ cup melted butter with ½ cup crumbs, and sprinkle over casserole.If using thinner bread (rather than buns), make two layers of the bread.