In a large skillet, heat olive oil over medium heat. Add the diced onion and diced green bell pepper. Sauté until they begin to soften, about 5 minutes.
Stir in the minced garlic and cook for an additional 1 minute until fragrant.
Add the ground beef to the skillet. Use a spatula to break it up as it cooks, until browned and fully cooked, about 5-7 minutes. Drain excess grease if necessary.
Mix in the Worcestershire sauce, paprika, salt, black pepper, and beef broth. Bring to a simmer, then reduce the heat to low.
Allow the mixture to cook for 5-10 minutes, stirring occasionally, until it thickens slightly.
Once thickened, sprinkle the shredded provolone cheese over the mixture. Cover the skillet and cook for another 2-3 minutes, or until the cheese is melted.
Toast the hamburger buns on a separate skillet or in a toaster while the cheese melts.
Serve the cheesy beef mixture on the toasted hamburger buns, garnishing with fresh parsley on top, if desired.