Heat a large skillet over medium heat and cook the ground beef until it browns, breaking it up as it cooks. Add the onion and green bell pepper and cook until they soften.
Stir in the tomato sauce, ketchup, brown sugar, and Worcestershire sauce. Let the mixture simmer for 5 minutes so the flavors combine and the sauce thickens slightly.
Transfer the beef mixture to an 8x8 baking dish and spread it into an even layer.
In a mixing bowl, whisk together the cornmeal, flour, and baking powder. Add the milk, egg, and melted butter and stir just until combined.
Pour the cornbread batter over the beef mixture and spread it gently to cover. Sprinkle the shredded cheddar cheese on top.
Bake at 400°F for 20 minutes until the topping is golden and a toothpick inserted in the center comes out clean.