Preheat the oven to 425°F and adjust the rack to the middle position.
In a bowl, mix the cottage cheese, Parmesan, garlic, and ¼ teaspoon black pepper.
In another bowl, combine the sausage, mushrooms, ¼ teaspoon salt, and ¼ teaspoon pepper.
Cover and microwave for about 9 minutes, stirring occasionally, until the sausage is cooked and mushrooms release their liquid.
Stir in the spinach and microwave for 1 more minute, until wilted.
Transfer mixture to a colander and drain for 5 minutes, pressing with a spoon to remove excess moisture.
Grease an 8-inch square baking dish.
Spread 1 cup of marinara sauce in the bottom of the dish.
Lay down 2 no-boil lasagna noodles, slightly overlapping if needed.
Add half the sausage mixture, half the cottage cheese mixture, and ½ cup shredded mozzarella.
Add 2 more noodles, 1 cup marinara sauce, the remaining sausage mixture, the remaining cottage cheese mixture, and another ½ cup mozzarella.
Top with the final 2 noodles, spread the remaining marinara sauce on top, and finish with the last 1 cup mozzarella.
(If making ahead, cover and refrigerate up to 24 hours. Increase covered baking time to 45 minutes.)
Cover tightly with greased foil and bake for 30 minutes, until bubbling at the edges.
Uncover and bake for 10 to 15 more minutes, rotating the dish halfway through, until the cheese is golden in spots.
Let cool for 15 minutes before serving.