Arrange the tomato and mozzarella slices on a platter or individual salad plates, overlapping the slices and fanning them out like a deck of cards.
Sprinkle with the salt and pepper.
Drizzle with the oil.
Garnish with the basil: Cut it into very thin slices or tear into bits and sprinkle on top or leave the leaves whole and tuck them here and there between the mozzarella and tomato slices. Serve immediately.