Preheat the oven. Heat the oven to 375°F. Lightly grease an approximately 11 x 8.5-inch deep baking dish.
Make the squash filling. Add the butternut squash puree, ricotta cheese, milk, salt, and nutmeg to a food processor or mixing bowl. Blend or stir until smooth and creamy. Add a little more milk if the mixture is too thick. Taste and adjust the seasoning.
Prepare the spinach filling. Combine the cooked spinach, ricotta, mozzarella, minced garlic, salt, and black pepper. Mix thoroughly and adjust the seasoning to taste.
Cook the noodles. Prepare the lasagna noodles according to the package directions. Drain and rinse with cold water. Trim the noodles if necessary so they fit your baking dish.
Start layering. Spread about one-third of the butternut squash mixture over the bottom of the prepared dish. Sprinkle with a light layer of mozzarella.
Add noodles and spinach. Arrange a layer of cooked lasagna noodles without overlapping. Spread half of the spinach mixture over the noodles and sprinkle with a little mozzarella.
Continue layering. Add another layer of noodles, followed by another one-third of the butternut squash mixture and a light sprinkle of mozzarella.
Add the final spinach layer. Place another layer of noodles in the dish. Spread the remaining spinach mixture evenly over the noodles and add a little more mozzarella.
Finish the lasagna. Add the final layer of noodles. Spread the remaining butternut squash mixture generously over the top. Sprinkle with Parmesan and the remaining mozzarella.
Season the top. Sprinkle the cheese with Italian seasoning, paprika, and dried basil.
Bake. Cover the dish tightly with foil and bake the Butternut Squash and Spinach Lasagna for 30 minutes.
Brown the cheese. Carefully remove the foil and bake for another 10 minutes, or until the cheese is melted and lightly golden.
Rest and serve. Let the lasagna rest for about 10–15 minutes before slicing. This helps the layers set and makes serving easier.