Heat the olive oil in a large skillet over medium-high heat, then add the sliced bell pepper, onion, and mushrooms. Sauté the vegetables for 5 to 7 minutes, stirring occasionally, until they are softened and have developed light brown spots.
Push the vegetables to one side of the skillet and add the thinly sliced beef to the empty side. Season the beef with kosher salt, black pepper, and garlic powder, then cook for 2 to 3 minutes without stirring to allow it to brown.
Stir the beef and vegetables together in the skillet and continue cooking for another 2 minutes, until the beef is fully cooked through and no longer pink.
Divide the hot beef and vegetable mixture into 8 equal portions and place each portion onto a slice of provolone cheese, allowing the heat to begin melting the cheese.
In a small bowl, stir together the mayonnaise, grated Parmesan cheese, and Italian seasoning to create a creamy sauce.
Place 2 lettuce leaves on a plate so they slightly overlap, creating a sturdy base. Spoon one portion of the cheesesteak mixture onto the center of the leaves, then drizzle with 1 tablespoon of the mayonnaise sauce.
Gently roll the lettuce leaves around the filling, tucking in the sides as you go to form a tight, burrito-style wrap. Repeat with the remaining ingredients to make 8 rolls total.
Serve the rolls immediately while the filling is still warm.