Add ground beef to a skillet and cook until brown crust forms. Break apart the meat and brown further.
Once cooked through, remove the beef from the pan, leaving fat behind.
Add onions, pepper, mushrooms, and butter to the skillet and cook until tender, stirring occasionally.
Add beef back to the pan, along with ketchup, worchestershire sauce, salt, and pepper.
In a small dish combine cornstarch and beef broth by adding dribbles of the broth to the cornstarch a little bit at a time to prevent lumps from forming.
Add cornstarch mixture to the skillet, stir, and cook until liquid reduces to a thick saucy consistency. If it is too runny, continue cooking to reduce further.
Lightly toast insides of hamburger buns, add sloppy joe mixture and top with provolone cheese.