1.Combine 1 tablespoon of the oil with garlic in small bowl. Place tomato, cut-side up, on oven tray; drizzle with oil mixture. Cook in covered barbecue, using indirect heat, following manufacturer’s instructions, about 20 minutes or until softened.
2.Combine radicchio with 2 tablespoons of the remaining oil in large bowl. Cook radicchio on heated oiled barbecue, uncovered, until browned all over; cool 5 minutes.
3.Combine vinegar and remaining oil in screw-top jar; shake well.
4.Arrange tomato, radicchio and rocket on large serving platter; sprinkle with cheese, drizzle with dressing.