Combine rosemary and next 4 ingredients in a bowl; stir with a whisk until blended. Brush ears of corn and the cut surfaces of the remaining vegetables with half of olive oil mixture, and set aside.
Coat grill rack with cooking spray; place on grill over medium-hot coals. Place vegetables, cut sides down, on rack. Cook 5 minutes; brush with remaining olive oil mixture. Turn vegetables over, and cook an additional 5 minutes or until tender. Remove from grill; cut each ear of corn into 6 pieces. Cut each onion slice into quarters. Cut remaining vegetable pieces in half.