Preheat the oven to 220 degrees C.
Put the tomatoes in a medium bowl and use your hands to crush them. Rinse the can with 1½ cups water and add it to the bowl.
In a pan on medium high heat, add the olive oil and garlic, ½ teaspoon of salt and cook for 1 minute. Add the tomato paste and stir. Add the crushed tomatoes with their juice and 4 large leaves of basil. Add the chicken, zucchini, and carrots. Bring the sauce to a boil; reduce the heat and simmer, stirring occasionally, until the sauce is thickened, about 40 minutes.
For the ricotta mixture: stir together the ricotta, eggs, ½ cup Parmesan cheese and salt and pepper in a bowl. Cover and refrigerate for at least 1 hour to allow flavors to blend.
Assemble the lasagna: Spread a thin layer of sauce on the bottom of a 22X33cm baking dish. Lay 4 of the noodles on the bottom, without overlapping. Spread with half of chicken mixture, one-third of the tomato sauce, one-third of the ricotta mixture, one-third of mozzarella and one-third of the Parmesan. Repeat with the remaining ingredients. Cover with foil and bake until bubbly and hot, about 30 minutes. Remove the foil and cook until the cheese begins to brown, about 15 minutes more. Allow to rest for 10 minutes so the lasagna will cut more easily. Garnish with the parsley. Serve.