To Make Tomato Sauce: Saute onion and garlic in olive oil over medium heat for about 10 minutes, or until translucent but not browned. Add thyme and carrot, cook 5 minutes over medium heat and add tomatoes. Bring to boil, lower heat to just bubbling and simmer 30 minutes, stirring occasionally. Season with salt to taste and set aside.
To Make Stuffed Zucchini: Preheat oven to 450 degrees.
Trim zucchini and cut in half lengthwise. Using a spoon or a melon baller, remove a canal down center of each zucchini half, leaving a 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 olive oil until just smoking. Add onion and garlic and cook over medium high heat until softened, about 6 to 7 minutes. Add zucchini pieces and crumbled lamb and cook until lamb is cooked through, about 10 minutes. Drain fat from lamb mixture and place in a large mixing bowl. Add eggs, half of the mint leaves and tomato sauce and mix well. Season both the mixture and the zucchini boats with salt and pepper. Stuff the lamb mixture into zucchini boats and pile high. Place in an oven-proof baking dish just large enough to hold the 8 pieces and sprinkle with bread crumbs. Bake for 20 to 25 minutes until crisp on top and remove. Serve warm or at room temperature with a chicory salad and sprinkle with remaining mint leaves.