Preheat grill on high. Cut the tomatoes in half and remove the pulp and seeds. Brush the cut side with olive oil along. Also brush the small grill grate or grill basket with olive oil. Place the tomatoes cut side down and cook with grill covered for about 4 minutes. On a serving dish, alternate slices of tomatoes and mozzarella. Sprinkle with basil and drizzle with balsamic glaze. Serve and enjoy.