To prepare Mozzarella Balls, place bread pieces in a food processor, and pulse until you have about 2 cups coarse bread crumbs. Stir in rosemary leaves and shaved garlic; season with salt and pepper. Place flour on a shallow plate; season with salt and pepper. Dip mozzarella in seasoned flour, shaking off excess. Dip mozzarella into egg, then coat completely in focaccia bread crumbs. Place on a tray; set aside in the refrigerator.

Preheat oven to 425 degrees F. To make Tomato Dipping Sauce, set tomatoes, onion, and garlic on a roasting tray. Drizzle with olive oil and season with salt and pepper. Roast for 15 to 20 minutes, until the tomatoes are slightly caramelized on the top. Remove from oven and transfer to a blender; puree, using a towel to cover the lid and hold down tightly. Transfer tomato mixture to a pot and simmer over low heat until thick and creamy. Season with salt and pepper.

Pour 4 inches oil into a large heavy pot and heat to 375 degrees F. Fry a few mozzarella balls at a time for 3 to 4 minutes, until golden brown and cheese is just beginning to melt. (Keep the oil hot; if the oil cools, the cheese will melt too much and the balls will fall apart.) Drain on paper towels. Season with salt. Serve with Tomato Dipping Sauce.