Melt the butter in a skillet over medium high heat.

Add in the onions, peppers and ground beef. Cook until the vegetables are tender and the beef is browned completely. Drain the extra fat off.

Stir the broth and cornstarch together in a bowl, and then pour over the meat.

Mix in the ketchup and Worcestershire sauce, as well as salt and pepper to taste. Simmer until the mixture is thickened.

Add in the cheese and stir until melted. Serve the sloppy joes on the buns.