Arrange alternating tomato and mozzarella slices on a serving platter, or place a tomato on an individual serving dish and top each piece of tomato with a slice of mozzarella. This may be done a few hours in advance. Keep refrigerated until ready to serve. Just prior to serving, chop the basil coarsely into thin strips. Sprinkle the basil over the tomato/mozzarella pieces. Drizzle a thin line of extra-virgin olive oil on top of the tomato-mozzarella combination. Follow with a few drops of balsamic vinegar per sliced tomato if desired and then add freshly ground pepper and salt to taste.