Preheat the oven to 450 degrees F.
Cut each of the zucchini in half crosswise and then slice lengthwise into 1/4-inch strips. Toss with 1 tablespoon of the oil and a pinch of salt, and spread on a baking sheet. Cut the portabellas into 1/4-inch strips, and then toss in the remaining 1 tablespoon oil and a pinch of salt and place on a separate baking sheet. Roast for 7 to 8 minutes, then flip and roast until tender and starting to brown, 4 to 5 minutes. The portabellas may take a few minutes longer than the zucchini. Cool the vegetables. Reduce the oven temperature to 350 degrees F.
While the vegetables roast, mix 1/2 cup of the Parmesan, the pepper, nutmeg, ricotta, eggs, basil and 1 teaspoon salt in a large bowl until well combined.
Spread 1 1/2 cups of the marinara in the bottom of a baking dish and top with an even layer of uncooked lasagna noodles (about 5). Top the noodles with 1 1/2 cups of the ricotta mixture, spreading as evenly as possible. Evenly distribute half of the roasted veggies over the ricotta and top with 2 cups of the spinach. Add another 1 1/2 cups of marinara and another layer of noodles. Repeat with another 1 1/2 cups ricotta, the other half of the roasted vegetables, half of the mozzarella slices, the remaining 2 cups spinach, 1 1/2 cups of marinara, and then another layer of noodles. For the final layer, spread the remaining 1 1/2 cups ricotta, another layer of noodles, 1 1/2 cups of marinara, the remaining mozzarella slices, and then top with the remaining 1/2 cup of Parmesan.
Bake for 1 hour covered with foil. Then remove the foil and bake until bubbly and beginning to brown, 20 to 25 minutes. Rest the lasagna 15 to 20 minutes before serving.