In large nonmetal dish or resealable food-storage plastic bag, mix vegetables and dressing; turn to coat.
Heat gas or charcoal grill. Remove vegetables from marinade. Place vegetables in grill basket (grill “wok”). Place on grill over medium-high heat. Cover grill; cook 10 to 15 minutes, stirring occasionally, until crisp-tender.
Sprinkle with cheese and basil.