Bring a large saucepan of water to a boil, reduce heat to medium, and cook red bell peppers in the boiling water until slightly softened, about 5 minutes. Drain and rinse peppers with cold water.
Stir eggs, 3 cups of spaghetti sauce, instant rice, onion, salt, Worcestershire sauce, and black pepper together in a bowl. Crumble ground beef into the mixture and stir until ground beef is thoroughly combined with sauce and rice mixture.
Stand peppers in a large baking dish and fill each pepper with beef mixture. Pour 2 cups spaghetti sauce over the peppers. Cover dish with aluminum foil.
Bake in the preheated oven until peppers are tender, the filling is set, and an instant-read meat thermometer inserted into the middle of a pepper reads at least 160 degrees F (70 degrees C), 55 to 60 minutes. Uncover and top each pepper with 1 tablespoon Cheddar cheese.