Heat grill. In pint jar with tight-fitting lid, combine all basting oil ingredients. Shake vigorously to blend. Place vegetables in 15x10x1-inch baking pan. Pour basting oil over vegetables, stir to coat.
When ready to barbecue, place vegetables, cut side down, on gas grill over medium-low heat or on charcoal grill 4 to 6 inches from medium-high coals. Cook 14 to 18 minutes or until crisp-tender, turning once and brushing with basting oil to keep surfaces moist. (Cooking time will vary according to size of vegetables.) Cut vegetables into bite-size pieces.