Slice a thin piece off the stem end of the tomato and discard. Remove a thin piece of flesh off the long side of the tomato to make it stable. Place wooden skewers or chopsticks along the sides of the tomato. Using a sharp knife, make 4 wedge slices into the tomato, until the blade of the knife hits the skewers/chopsticks.
Lay a small basil leaf on top 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 this process with the remaining tomatoes, mozzarella and basil until all 4 tomatoes have been stuffed.
Place the tomatoes onto a serving platter. Drizzle generously with the oil and balsamic glaze. Sprinkle with flakey sea salt and freshly cracked black pepper to serve.
Use pre-sliced fresh mozzarella cheese for this recipe. A thin log is the best choice.