PREHEAT barbecue to medium heat. Place potatoes and carrots in microwaveable bowl. Add water; cover. Microwave on HIGH 5 to 7 min. or until potatoes are crisp-tender; drain well. Meanwhile, mix 1/3 cup Parmesan cheese and the dressing. Add to potato mixture; mix lightly.

SPOON onto centre of 20-inch-long piece of heavy-duty foil sprayed with cooking spray. (Or, use a double layer of regular foil.) Bring up foil sides. Double fold top and ends to seal packet, leaving room for heat circulation inside. Place on top shelf of barbecue.

GRILL 15 to 20 min. or until vegetables are tender. Cut slits in foil to release steam. Open packet. Sprinkle potato mixture with parsley and the 1 Tbsp. Parmesan cheese.