Preheat grill to medium heat. Toss tomatoes with basil and 2 TBSP. of the dressing; set aside. Heat remaining dressing in skillet on medium heat. Add mushrooms; cook and stir 5 min. or until tender and liquid has evaporated. Stir in 1/2 of the tomato mixture and cheese. Cool slightly.
Mix meat and mushroom mixture. Shape evenly into 4 patties. Grill patties 7 to 9 min. on each side or until cooked through.
Cover bottom halves of rolls with burgers. Top with remaining tomato mixture and top halves of rolls.