1Heat gas or charcoal grill. In small bowl, combine mayonnaise and 2 teaspoons salad dressing; blend well. Set aside. Sprinkle mushroom caps with salt and pepper.
2When grill is heated, place mushrooms on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cover grill; cook 5 to 8 minutes or until thoroughly heated, turning once.
3Meanwhile, brush cut sides of rolls with 1/4 cup salad dressing. During last 1 to 2 minutes of cooking time, place cheese on mushrooms and place rolls, cut side down, on grill to toast.
4Spread toasted rolls with mayonnaise mixture. Serve cheese-topped mushrooms in rolls.