In a skillet over medium heat, cook the ground beef until browned, breaking it apart with a spatula.

Add the chopped onion, green bell pepper, and minced garlic. Cook until the vegetables are soft, about 5 minutes.

Stir in the beef broth, Worcestershire sauce, salt, and black pepper. Bring to a simmer and cook for 10 minutes, allowing the mixture to thicken.

Remove from heat and stir in the shredded provolone cheese until melted.

Spoon the mixture onto the toasted hamburger buns and serve immediately.