Cook the Beef
Heat a large skillet over medium heat. Add the ground beef and cook, breaking it up with a spatula, until browned and fully cooked. Drain any excess grease and set aside.
Sauté the Vegetables
In the same skillet, add the diced onion, bell pepper, and mushrooms (if using). Cook for 4-5 minutes, or until the vegetables are tender. Add the minced garlic and cook for an additional minute.
Combine and Season
Return the cooked beef to the skillet. Stir in the beef broth, Worcestershire sauce, ketchup, Dijon mustard, salt, and black pepper. Simmer for 3-4 minutes, allowing the flavors to meld together.
Add the Cheese
Reduce the heat to low and sprinkle the shredded provolone cheese over the beef mixture. Stir until the cheese is melted and creamy.
Assemble the Sloppy Joes
Spoon the cheesy beef mixture onto the toasted sandwich buns. Serve immediately while hot.