Cut the tomatoes in wedges or fat slices. Small cherry tomatoes can be left whole. Tear the basil leaves into large pieces or slice them in a chiffonade. (To make a chiffonade, roll the large leaves into a tight cylinder and then cut in very thin strips.) You should have about ⅓ cup.
Combine half the basil with the tomatoes, onion slices, olive oil, vinegar, salt and black pepper to taste, and mix very gently. Use your hands so the tomatoes do not get bruised. Arrange the salad on a platter, scatter the remaining basil over the top, and garnish with shavings of cheese or a few olives if you like.