Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Mix steak and meat tenderizer together in a bowl.
Heat olive oil in a skillet over medium heat. Add onion and bell pepper; cook and stir until slightly softened, about 3 minutes. Stir in steak mixture; cook and stir until flavors combine, about 3 minutes. Mix in Italian seasoning and pepper; add mushrooms. Cook and stir until steak is mostly browned, about 3 minutes.
Spoon steak mixture onto lower half of dinner rolls until covered; top with provolone cheese. Place onto a baking sheet.
Broil in the preheated oven until cheese is melted, 1 to 3 minutes; remove from broiler. Place dinner roll tops onto melted provolone cheese; broil until tops are toasted, 1 to 2 minutes.