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