Cut a 1/4-inch slice from the stem end of each tomato. Using a spoon, carefully scoop out core, seeds, and pulp, leaving up to a 1/2-inch-thick shell. Discard pulp. Sprinkle tomato shells with the 1/4 teaspoon sea salt and the 1/8 teaspoon pepper. Stand tomato shells on a plate; set aside.
For dressing, in a screwtop jar, combine olive oil, vinegar, and sugar. Cover; shake well. Reserve 1-1/2 tablespoons of dressing. Spoon remaining dressing into tomato shells.
In a medium bowl combine mozzarella, red onion, basil, and reserved dressing; toss to mix. Spoon cheese mixture into tomato shells. Cover and refrigerate until ready to serve, up to 2 hours. To serve, place stuffed tomatoes on individual plates. Sprinkle with additional salt and pepper. Makes 4 servings.