Heat olive oil in a large skillet over medium heat.
Add the diced onion, green bell pepper, and mushrooms. Sauté for about 5 minutes until the vegetables are softened.
Add minced garlic and cook for an additional minute.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and fully cooked, about 6-8 minutes. Drain any excess fat.
Stir in Worcestershire sauce, salt, black pepper, and paprika. Mix well and let it simmer for 2-3 minutes to combine the flavors.
Remove the skillet from heat and stir in the shredded provolone cheese until melted and well combined.
Toast the hamburger buns lightly under the broiler or in a toaster.
Spoon the cheesesteak mixture onto the bottom half of each bun, then top with the other half.
Serve immediately while warm.