Bring grill to high heat.
Drizzle and brush 1/2 teaspoon of olive oil onto cut sides of each romaine half. Sprinkle with salt and pepper.
Lay romaine halves on grill, cut sides down. Grill until slightly charred, 1 to 2 minutes.
Plate romaine halves, cut sides up. Top with tomato, onion, cheese and basil.
In small bowl, whisk vinegar with remaining 2 teaspoons of olive oil. Drizzle atop salad and enjoy.