1. Pull off tough outer leaves of romaine bunches, and discard; cut bunches in half lengthwise, keeping leaves intact. Peel onion, and cut in half vertically, keeping core (root end and top) intact. Cut each half into 4 wedges. Brush lettuce and onion evenly with olive oil.
2. Coat cold cooking grate evenly with cooking spray, and place on grill over medium heat (300° to 350°). Place onion wedges on cooking grate, and grill, covered with grill lid, 3 to 4 minutes on each side or to desired degree of doneness. Remove onion wedges.
3. Place romaine halves, cut sides down, on cooking grate. Grill, without grill lid, 2 to 3 minutes or just until wilted.
4. Divide grilled lettuce, cut sides up, evenly among serving plates. Top each with 1 onion wedge (separate into slices, if desired), and drizzle with Buttermilk-Chive Dressing. Sprinkle evenly with shaved Parmesan cheese and salt and pepper to taste. Serve immediately.