Preheat your oven to 350°F (175°C).

Cook the ground beef in a large skillet over medium heat, breaking it up as it cooks. Once browned, drain any excess fat.

Add the onion and bell pepper to the skillet with the beef, cooking until the vegetables soften, about 5 minutes.

Stir in the Worcestershire sauce, brown sugar, mustard, ketchup, water, salt, and pepper. Let the mixture simmer for approximately 5 minutes until it thickens slightly. Add a little more water if needed to reach the desired consistency.

Prepare the cornbread topping by combining the corn muffin mix, milk, vegetable oil, and egg in a mixing bowl. Stir just until the ingredients are incorporated; the batter will be slightly lumpy. Set this aside.

Assemble the casserole by spreading the sloppy joe mixture evenly in a greased 9x9-inch baking dish. Pour the cornbread batter over the top, spreading it out to cover the beef mixture.

Bake in the preheated oven for 25 to 35 minutes, or until the cornbread is golden brown and fully cooked.

Immediately sprinkle the shredded cheddar cheese on top of the casserole as soon as it comes out of the oven, allowing it to melt over the cornbread.

Let the casserole rest for a few minutes before serving to make it easier to cut and serve.