Melt butter in a large pot over medium heat. Stir in all bell peppers, onion, and garlic until everything is slightly soft (approximately 2 minutes). Stir in ground beef and cook until it is browned, stirring often. Drain grease. Season with taco seasoning packet.
Mix diced tomatoes, rice, Worcestershire sauce, black beans, tomato sauce, and broth into beef/bell pepper mixture and bring to a simmer. Cook until rice is tender, about 20 minutes, stirring occasionally. Pour mixture into a large casserole dish. Top with cheddar cheese.
Bake in oven until casserole is heated through, about 45 minutes.