Preheat oven to 375°F (190°C).
Cook lasagna noodles according to package instructions. Drain and set aside.
Heat olive oil in a skillet over medium heat. Sauté onion until translucent, then add garlic and cook for 1 minute.
Add spinach to the skillet and cook until wilted. Remove from heat.
In a bowl, whisk together pumpkin puree, milk, nutmeg, salt, and pepper to create the sauce.
Spread 1/2 cup of the sauce on the bottom of a 9x13-inch baking dish.
Layer 3 noodles, followed by 1/3 of the pumpkin sauce, half of the spinach mixture, half of the cottage cheese, and 1/2 cup mozzarella.
Repeat with another layer of noodles, sauce, spinach, cottage cheese, and mozzarella.
Top with final layer of noodles, remaining sauce, 1/2 cup mozzarella, and Parmesan.
Cover with foil and bake for 25 minutes. Remove foil and bake an additional 15 minutes until golden and bubbly.
Let rest 10 minutes before serving.