Slice a thin piece off the stem end of the tomato and discard it. Remove a thin piece of flesh from the long side of the tomato to make it more stable.
Place chopsticks along the sides of the tomato. Using a sharp knife, make 6 wedge slices into the tomato, until the blade of the knife hits the chopsticks.
Lay a small basil leaf on top of each piece of mozzarella cheese.
Gently push the slice of cheese and basil leaf into each crevice cut in the tomato. The cheese should be flush with the top of the tomato. Repeat with the remaining tomatoes, mozzarella, and basil until all four tomatoes have been stuffed.
Sprinkle a few more basil leaves on top of each tomato.
Drizzle with olive oil and balsamic vinegar, and then season with sea salt and freshly cracked black pepper to taste.