Cut tops off of peppers to create 5 "bowls"; set tops aside. Discard seeds from bottoms. Boil pepper "bowls" in water until softened. Remove stems from tops and chop remaining pepper to add to chopped onions and mushroom mixture. Brown ground beef and remove from pan. Add butter, onions, mushrooms, and chopped peppers. Cook until soft. Add meat back to pan. In a small bowl, mix beef broth and cornstarch. Add ketchup, Worcestershire sauce, salt, pepper, and beef broth mixture to pan. Cook for about 5 minutes. Turn off heat and add cheese. Put green pepper bowls in a baking pan. Fill each with meat mixture. Top each pepper with a slice of cheese, optional. Bake at 350 degrees for 20 minutes.