Heat a large skillet over medium-high heat. Add the ground beef, diced green bell pepper, and diced onion. Cook until the beef is browned and vegetables are tender, about 8 to 10 minutes. Drain any excess fat.

In a small bowl, whisk together the beef broth, Worcestershire sauce, cornstarch, salt, and black pepper. Pour the mixture into the skillet with the beef and vegetables.

Simmer the mixture for 3 to 5 minutes until the sauce thickens and coats the beef evenly. Remove the skillet from the heat.

Lay the provolone cheese slices directly over the hot beef mixture in the skillet. Cover with a lid for 1 to 2 minutes until the cheese is perfectly melted.

Scoop the cheesy beef mixture onto toasted hamburger buns and serve hot.