Prepare a charcoal or gas grill for high heat (450° to 550°; you can hold your hand 5 in. above cooking grate only 2 to 4 seconds). Brush 2 tbsp. oil over cheese and onion. Grill, turning once, until grill marks appear, about 8 minutes. Cut onions in half.
Fill pita halves with equal amounts of cheese, onions, peppers, and pepperoncini. Brush a little oil on outside of pitas, then grill, turning once, until grill marks appear and bread is toasted, about 4 minutes. Serve with mixed olives and a green salad.
Note: Nutritional analysis is per 2 pita halves.