Remove the top and the core of the tomato. Finely chop any edible parts of the top and core and reserve. Season the inside of the tomato with salt and pepper. Combine the onion, basil, mozzarella, and olives in a bowl. Drizzle with olive oil and season with salt and pepper, to taste. Fill the cavity of the tomato with the onion mixture. Serve the stuffed tomato on a bed of tomato water and garnish with the reserved chopped tomato.
Combine all ingredients in a blender or food processor. Add just enough olive oil for flavor and season with salt and pepper, to taste.