Preheat the oven to 425°F. Coat an 8x8 inch baking pan with cooking spray.
Coat a large skillet with cooking spray and heat over high heat. Add spinach, stirring until leaves wilt, about 5 minutes. Place in a colander.
Coat skillet with cooking spray again and heat over high heat. Cook zucchini in batches, 2 to 3 minutes per side; drain on paper towels.
Squeeze excess moisture from spinach. Mix spinach, ricotta, egg white, ¼ cup of the Parmesan, basil, ½ teaspoon of salt and nutmeg in a bowl; set aside.
In a food processor, puree tomatoes, onion, garlic, pepper, and remaining ½ teaspoon salt. Spread half of the sauce on the bottom of the prepared pan. Layer zucchini on top, then half of the ricotta mixture. Add a layer of zucchini and remaining half of ricotta and sauce. Sprinkle with mozzarella and remaining ¼ cup Parmesan.
Bake, uncovered, until cheese browns, about 30 minutes. Cool slightly before cutting.