In a large skillet, cook the ground beef over medium heat until browned.
Add the diced onion and green bell pepper, and cook for a few more minutes until the vegetables are tender.
Stir in the beef broth, ketchup, Worcestershire sauce, salt, and black pepper.
Simmer for about 10 minutes until the mixture thickens.
Stir in the shredded provolone cheese until melted.
Spoon the mixture onto hamburger buns and serve hot.