Cook the beef: In a large skillet, heat olive oil over medium heat. Add ground beef and cook until browned, breaking it apart with a spoon. Drain any excess fat.

Sauté the vegetables: Add the onion and bell pepper to the skillet and cook for 4-5 minutes, until softened. Add the garlic and cook for another minute.

Make the sauce: Stir in the beef broth, Worcestershire sauce, ketchup, and Dijon mustard. Let it simmer for 5-7 minutes, until the mixture thickens and becomes saucy. Season with salt and pepper to taste.

Assemble the sandwiches: Split the sandwich buns and lightly toast them. Spoon the beef and vegetable mixture onto the buns, then top each with shredded provolone cheese.

Melt the cheese: Place the open sandwiches under a broiler for 1-2 minutes, or until the cheese is melted and bubbly.

Serve: Garnish with fresh parsley if desired, and serve immediately.