Break up and brown ground beef in a pan/skillet.
Remove beef from the pan, leave the fat in the pan. Add butter once it is melted down add in onions, bell peppers, and mushrooms.
Allow to cook for a few minutes, allowing the vegetables become tender and add beef back into the pan.
In small dish mix cornstarch into beef broth, making sure it is completely combined.
Add ketchup, Worcestershire sauce, salt, pepper and the beef broth mixture.
Allow to simmer for several minutes stirring occasionally so sauce thickens to your desired consistency.
Remove from heat and add in cheese mixing until it is melted.
Toast buns, scoop plenty of sloppy joe meat on each bun and enjoy!