Heat a large skillet over medium-high heat. Add the olive oil and mushrooms and saute until lightly browned, about 10 minutes. Stir in the garlic. Add the spinach and cook, stirring, until it wilts. Remove from the heat and set aside.
Meanwhile, trim the ends of the zucchini. Using a knife, carefully slice the zucchini lengthwise into thin strips, about 1/16 inch thick. If the zucchini looks watery, lay the slices on paper towels to absorb excess moisture before using.
Grate the mozzarella cheese and set aside.
Cut the basil into a chiffonade by stacking the leaves on top of one another, rolling them tightly and then cutting across. Finely chop the parsley. In a medium bowl, combine the herbs, cottage cheese, 1/2 cup of the Parmesan, the eggs, salt and pepper and stir well.
To assemble the lasagna, place a third of the mushrooms and spinach mixture over the bottom of a 13-by-9-inch baking dish. Spoon a layer of marinara on top and cover with half of the zucchini strips, carefully overlapping the edges. Spoon half of the cottage cheese mixture onto the zucchini and spread to distribute evenly. Sprinkle half the mozzarella on top of the cottage cheese mixture. Repeat the process above, layering the mushrooms and spinach, marinara, the remaining zucchini strips, cottage cheese, and mozzarella into the dish. Top with the remaining mushrooms and spinach, followed by a final layer of marinara.
Sprinkle the remaining 1/2 cup of the Parmesan over the top and bake until the lasagna is hot and bubbly, about 40 minutes. Allow to stand for 35 minutes before cutting into squares.