Cut half the tomatoes into thick slices and the other half into wedges. Arrange the slices on a large serving plate, slightly overlapping each other.
Put the tomato wedges into a bowl and drizzle with olive oil and balsamic vinegar. Season to taste with salt and pepper. Mix carefully and arrange on top of the tomato slices.
Add the basil leaves and mozzarella balls to the tomato wedges. Drizzle the salad with more olive oil and balsamic vinegar, season to taste with salt and pepper and serve.