- In a large skillet, heat the olive oil over medium heat. Add the diced onion and green bell pepper, cooking until softened, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant. 
- Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and fully cooked, about 6-8 minutes. Drain excess fat if necessary. 
- Stir in the Worcestershire sauce, soy sauce, Dijon mustard, and beef broth. Season with salt and pepper to taste. Bring the mixture to a simmer and let it cook for about 10 minutes, allowing the flavors to meld and the sauce to thicken slightly. 
- Remove the skillet from heat and stir in the shredded provolone cheese until melted and well combined. 
- Serve the cheesy beef mixture on hamburger buns, and enjoy your delicious Philly Cheesesteak Sloppy Joes!