Soak bread in lukewarm water, squeeze well and combine with ground beef and egg, season with salt and pepper. Peel onion and garlic and chop finely, add to meat mixture. Rinse and shake dry basil, pluck off leaves and set some for garnishing, chop the rest finely. Drain mozzarella and dice finely. Add basil and cheese to meat mixture.
Blanch tomatoes in hot water briefly, rinse in cold water and peel. Quarter and remove seeds, dice and mix with meat mixture. Make meatballs out of the mixture. Heat olive oil in a pan and cook meatballs for about 10 minutes on all sides. Arrange on plates and garnish with remaining basil. Serve immediately.