Preheat oven to 450 degrees F.
Trim the zucchini and cut in half lengthwise. Using a spoon or melon baller, remove the flesh making a canal down the center of each zucchini half, leaving 1/4-inch all around and the ends closed. Roughly chop the excess zucchini flesh and set aside.
In a 10 to 12-inch saute pan, heat the olive oil until just smoking. Add the onion and garlic and cook over medium-high heat until softened, about 6 to 7 minutes. Add the zucchini pieces and crumbled lamb and cook until the lamb is cooked through, about 10 minutes. Drain the fat from the lamb mixture and place in a large mixing bowl. Add the eggs, half of the mint leaves and the tomato sauce and mix well. Season both the mixture and the zucchini boats with salt and pepper. Stuff the lamb mixture into the zucchini boats and pile it high. Place in an oven-proof baking dish just large enough to hold all the zucchini and sprinkle with bread crumbs. Bake for 20 to 25 minutes, until crisp on top, and remove. Serve warm or at room temperature and sprinkle with remaining mint leaves.
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.
Recipe copyright 2000, Mario Batali. All Rights Reserved.