POUR 2 Tbsp. of the dressing over mushrooms in shallow dish; cover. Refrigerate 1 hour to marinate. Remove mushrooms from marinade; discard marinade.
PREHEAT barbecue to medium-high heat. Grill mushrooms 5 min. on each side or until tender.
COVER bottom halves of rolls with spinach and tomatoes; drizzle with remaining 2 Tbsp. dressing. Cover with mushrooms and tops of rolls.