In a large skillet over medium-high heat, brown the ground beef. Drain excess fat and set aside.
In the same skillet, sauté the diced onion and bell pepper until softened, about 5-7 minutes. Add minced garlic and cook for an additional minute.
Return the cooked beef to the skillet. Stir in Worcestershire sauce and beef broth. Season with salt and pepper. Simmer for 5-10 minutes until the sauce thickens.
Layer provolone cheese over the beef mixture, cover with a lid, and let the cheese melt. Stir to combine.
Toast sandwich buns on a baking sheet or in a skillet.
Spoon the beef mixture onto the toasted buns and serve immediately.