Add 1 teaspoon oil to nonstick pan and sauté peppers and onions until tender. Remove to a plate and set aside.
Add shaved steak to skillet and cook over medium heat until browned. Add worcestershire sauce and return peppers and onions to pan. Place provolone cheese slices over meat mixture and cover to allow cheese to melt.
Heat pita according to pkg directions then divide dressing between the the 2 rounds. Top each round with ½ of the meat mixture and serve.