Rub the romaine halves all over with olive oil and balsamic vinegar and place cut-side down on a hot grill. Grill for a few minutes until the lettuce begins to char. When you start to see charring, flip the halves over and grill for a few minutes on the other side. When the second side is charred to your liking, take both romaine halves off the grill. Sprinkle with salt and pepper and drizzle with more balsamic vinegar before serving, if you like.