Cut romaine hearts in half lengthwise, keeping leaves intact. Cut red onion crosswise into 1/2-inch slices, keeping rings intact; brush with olive oil, and set aside.
Coat food grater evenly with vegetable cooking spray, or brush lightly with vegetable oil. Place food on grate gril over medium heat (300º to 350º).
Place romaine halves, cut side down, on food grate. Grill, uncovered, 3 to 5 minutes or until just wilted. If desired, rotate halves once to get crisscross grill marks. Brush warm romaine halves with Buttermilk-Chive Dressing, coating lightly.
Place two romaine halves on each of 4 salad plates. Sprinkle with salt and pepper to taste. Top each evenly with onion slices and freshly shaved Parmesan cheese. Serve immediately with remaining Buttermilk-Chive Dressing.