1. In a large skillet, heat olive oil over medium heat. Add zucchini, carrot, mushrooms, and garlic; cook for 5 to 6 minutes or until vegetables are tender. Add spinach, stirring until spinach wilts. Cook, stirring frequently, until most of the liquid has evaporated. Stir in basil, salt, and pepper; set aside.
2. In a medium bowl, combine ricotta, 1 cup Parmigiano-Reggiano, and eggs; set aside.
3. Preheat oven to 350°F. Spray a 4-quart baking dish with nonstick cooking spray. Spread 1/2 cup pasta sauce in baking dish. Top with 4 lasagna noodles. Spread one-fourth of ricotta mixture over noodles. Top with half of vegetable mixture and 1 cup pasta sauce. Layer one-fourth of provolone over sauce. Top with 4 lasagna noodles. Spread with one-fourth ricotta mixture.
4. Combine chicken and shredded mozzarella cheese. Spread half of chicken mixture over ricotta.
5. Top with 1 cup pasta sauce, one-fourth of provolone, and 4 lasagna noodles. Spread one-fourth of ricotta mixture over noodles. Top with remaining chicken mixture, 1 cup pasta sauce, one-fourth of provolone, and 4 lasagna noodles. Spread with remaining ricotta mixture, remaining vegetable mixture, remaining 1 cup sauce, and remaining provolone cheese. Sprinkle with remaining 1 cup grated Parmigiano-Reggiano cheese. Bake for 45 to 60 minutes or until hot and bubbly.
6. Let stand for 10 minutes before serving.