In a large skillet, heat the olive oil over medium heat. Add the diced onion and green bell pepper, and sauté for about 5 minutes until softened.
Add the minced garlic and sliced mushrooms to the skillet, cooking for an additional 3-4 minutes until the mushrooms are tender.
Increase the heat to medium-high and add the ground beef. Cook until browned, breaking it apart with a spatula, about 5-7 minutes. Drain any excess fat.
Stir in the Worcestershire sauce, soy sauce, and beef broth. 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.
Reduce the heat to low and stir in the shredded provolone cheese until melted and creamy. Season with salt and pepper to taste.
Serve the cheesy beef mixture on hamburger buns, garnished with chopped parsley if desired.