Vegetable Lasagna

Two 15-ounce containers part-skim ricotta 2 large eggs 1 teaspoon kosher salt, plus more for seasoning 1/2 teaspoon cracked black pepper, plus more for seasoning One 10-ounce package frozen chopped spinach, thawed, excess moisture squeezed out 2 cups shredded mozzarella cheese 1 1/2 cups shredded Parmesan 1 cup fresh basil leaves, torn 1 tablespoon extra-virgin olive oil 3 cloves garlic, minced 1 yellow onion, diced 3/4 cup shredded carrot 1 yellow squash, diced 1 zucchini, diced 6 cups store-bought or homemade marinara sauce 12 no-boil lasagna noodles (8 ounces)