Preheat grill to medium-high (400 degrees to 450 degrees F).
Combine vegetables, basil, vinegar, oil, garlic, salt and pepper in a large bowl; marinate at room temperature 15 to 20 minutes. Stack 2 sheets of Reynolds Wrap® 18-inch Wide Heavy Duty Aluminum Foil on a cookie sheet or tray. Turn up sides of foil to form a rim.
Place vegetables in an even layer on foil. Slide foil from cookie sheet onto grill.
Grill 8 to 10 minutes in covered grill, turning frequently, until vegetables are crisp-tender. Slide foil from grill onto a cookie sheet for transporting to serving table.