Heat a large skillet over medium heat and cook ground beef with chopped onion until beef is browned and onions are tender, breaking up the meat.
Add minced garlic and cook for one more minute.
Stir in tomato sauce or ketchup, Worcestershire sauce, brown sugar if using, mustard, salt, pepper, and diced bell peppers if desired.
Simmer the mixture for 5 to 8 minutes until the sauce thickens.
Preheat oven to 350 °F (180 °C).
Spread the beef mixture evenly in a baking dish.
Spread mashed potatoes over the beef mixture into an even layer.
Dot the mashed potatoes with butter and sprinkle with shredded cheese if desired.
Bake for 20 to 25 minutes until the topping is heated through and lightly golden.
Let cool slightly before serving warm.