Remove cheese from brine, and cut into 12 slices; sprinkle tomato slices evenly with salt. Alternate tomato and cheese slices on a platter; drizzle with olive oil. Cover and chill 4 hours. Just before serving, sprinkle with freshly ground pepper and basil.
Note:*Fresh mozzarella is a soft white cheese available at gourmet grocery stores or cheese shops. Sometimes it's packed in brine, a strong solution of water and salt useed for pickling or preserving foods.