Preheat the Oven
Preheat oven to 400°F (200°C). Position rack in upper-middle.
Cook the Spinach
Melt 3 tablespoons butter in a large saucepan. Add garlic and cook 30 seconds. Add spinach in batches until wilted. Stir in 1 cup heavy cream. Simmer 15 minutes until thickened. Add nutmeg, salt, and pepper.
Prepare Cottage Cheese Mixture
In a food processor, blend cottage cheese, egg, and 6 tablespoons parsley until smooth like ricotta. Combine with spinach mixture in a large bowl.
Soften Noodles
Soak lasagna noodles in warm water for 15 minutes. Drain and lay flat to dry.
Cook Mushroom Mixture
In the same pot, melt 3 tablespoons butter. Add mushrooms and cook until liquid evaporates, about 10 minutes. Add shallots and thyme; cook 2 minutes. Stir in soy sauce and lemon juice. Add remaining heavy cream and simmer 3 minutes. Season to taste.
Make Cheese Sauce
Melt remaining 2 tablespoons butter. Whisk in flour and cook until lightly golden. Slowly whisk in milk until smooth. Simmer until thickened. Remove from heat and stir in 2/3 of mozzarella and all Parmesan. Season to taste.
Assemble the Creamy Spinach and Mushroom Lasagna
Butter a 8x13-inch baking dish. Spread 1 cup cheese sauce on bottom. Layer 3 noodles, half mushroom mixture, 3 noodles, half spinach mixture, 3 noodles. Repeat layers ending with noodles. Pour remaining cheese sauce over top. Sprinkle remaining mozzarella.
Bake
Bake for 20 minutes until bubbling. Broil 3–5 minutes until lightly browned.
Rest and Serve
Cool 10 minutes before slicing. Garnish with parsley.