Preheat oven to 375°F. Generously coat a 9-by-13-inch baking dish with cooking spray.

Heat 2 tablespoons oil in a large skillet over medium-high heat. Add mushrooms, garlic, salt and pepper and cook, stirring occasionally, until the mushrooms are tender and starting to brown, 6 to 8 minutes. Transfer to a small bowl.

Heat the remaining 1 tablespoon oil in the pan and add half the spinach. Cook, stirring frequently, until wilted, about 3 minutes. Add the remaining spinach by the handful and cook until it's all wilted, about 2 minutes more. Press the spinach to the side of the pan, squeezing out as much water as possible, and cook until the water is evaporated, 2 to 3 minutes more. Remove from heat.

Mix egg, ricotta, 1 cup mozzarella and 1/2 cup Parmesan in a medium bowl. Combine the remaining 1/2 cup each mozzarella and Parmesan in a small bowl. Spread 1 cup sauce in the prepared baking dish and top with a layer of 3 noodles. Spread 1 cup of the ricotta mixture over the noodles and top with the mushrooms. Spread the spinach over the mushrooms and top with another 1 cup sauce. Layer on the remaining 3 noodles, followed by the remaining ricotta mixture. Layer zucchini on top, shingling if necessary, and spread the remaining sauce over the zucchini. Top with the reserved mozzarella mixture.

Bake the lasagna until bubbly and the cheese is beginning to brown, about 45 minutes. Let cool for at least 10 minutes before slicing. Garnish with basil and/or parsley, if desired.