Use ripe tomatoes that are still slightly firm in this side dish. Very ripe tomatoes will overcook and become mushy.
Soak wood chips in water 30 minutes; drain well.
Prepare grill for indirect grilling, heating one side to high and leaving one side with no heat. Place 1 cup wood chips on hot coals. When chips begin to smoke, coat grill rack with cooking spray, and place on grill. Place tomato halves, cut sides down, on unheated side of grill. Cover and cook 18 minutes or just until tomatoes are tender. Add additional chips halfway through cooking time, if necessary.
Place tomatoes, cut sides up, on a serving platter; drizzle with oil. Combine parsley and remaining ingredients; sprinkle over tomatoes. Serve warm.