Heat a large skillet over medium-high heat. Break ground beef into pieces and add to skillet; cook and stir until about half of the beef is browned, 3 to 5 minutes. Stir red bell pepper, orange bell pepper, and green bell pepper into the beef; continue to cook and stir until the beef is entirely browned, about 5 minutes more. Drain and discard grease.
Mix tomato sauce and brown sugar together in a bowl; pour over the beef mixture. Stir rice into the beef mixture and stir; transfer to a 9x13-inch baking dish. Sprinkle Cheddar cheese over the mixture.
Bake in preheated oven until the cheese is bubbling, about 30 minutes. Cool dish 5 minutes before serving.