In small bowl, combine pepperochini, mayonnaise and mustard; spread over bread.
Layer bread with cheese, salami, ham, tomato, lettuce, onion, Italian dressing and cheese. Close up sandwich.
Spray a preheated Panini grill with cooking spray. Place sandwiches on grill; spray tops of sandwiches with additional cooking spray. Grill until bread is golden brown and cheese is melted (about 5 minutes).