In a shallow bowl, soak the bread cubes in enough water to cover. Remove the bread cubes and squeeze by hand to wring excess moisture.
In a large bowl, combine the bread, beef, eggs, garlic, pecorino, parsley, pine nuts, salt and pepper and mix by hand to incorporate bread into meat. With wet hands, form the mixture into 12 to 15 meatballs, each of a size somewhere between a tennis ball and a golf ball. In a large, heavy-bottomed skillet, heat the oil until almost smoking. Add the meatballs, working in batches if necessary to avoid overcrowding the pan, and cook until deep golden brown on all sides, about 10 minutes.
In a clean pan add the tomato sauce and reduce the heat to a simmer. Add all meatballs, cook for 10 minutes and serve.
In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion and garlic and cook until soft and light golden brown, about 8 to 10 minutes. Add the thyme and carrot and cook 5 minutes more, until the carrot is quite soft. Add the tomatoes and juice and bring to a boil, stirring often. Lower the heat and simmer for 30 minutes until as thick as hot cereal. Season with salt and serve. This sauce holds 1 week in the refrigerator or up to 6 months in the freezer. Yield: 4 cups