Using a food processor, combine 2 cups of mashed butternut squash, 1 cup ricotta cheese, 1/2 cup milk, 1/4 teaspoon salt, and 1/4 teaspoon ground nutmeg. Blend until the mixture is very creamy, adding more milk if needed. Taste and adjust the salt if necessary. Set aside for layering later.
In a mixing bowl, combine the cooked and well-drained spinach with 1 cup ricotta cheese, 1 cup shredded mozzarella cheese, 2 minced garlic cloves, 1/4 teaspoon salt, and black pepper to taste. Mix thoroughly until well combined. Taste and adjust salt and pepper as needed. Personally, I enjoy adding a squeeze of lemon juice if I have any, as it brightens the filling.
Bring a very large pot of water to a boil. Cook the lasagna noodles according to package instructions until al dente. Rinse the noodles in cold water and drain well. Trim the noodles to fit your baking dish, if necessary.
Preheat your oven to 375°F and lightly grease an 11 x 8.5 x 3 inch baking dish with olive oil or non-stick spray. Begin layering by spreading 1/3 of the butternut squash filling (from Step 1) on the bottom. Sprinkle lightly with mozzarella cheese, then add a layer of cooked lasagna noodles (from Step 3), without overlapping. Spread half of the spinach filling (from Step 2) over the noodles, sprinkle lightly with mozzarella cheese, and add another layer of noodles. Add another 1/3 of the butternut squash filling, sprinkle with mozzarella, and top with more noodles. Then, spread the remaining spinach filling, top with mozzarella, and add the final layer of noodles.
Spread the last 1/3 of the butternut squash filling (from Step 1) over the final layer of noodles. Sprinkle with 1/2 cup grated Parmesan cheese and the remaining mozzarella cheese (about 1/2 cup). Generously sprinkle with Italian seasoning, paprika, and dried basil. I like to be a little extra generous with the herbs and spices on top for a beautiful, flavorful crust after baking.
Cover the prepared baking dish with foil and bake in the preheated oven at 375°F for 30 minutes. After that, remove the foil and bake uncovered for an additional 10 minutes, or until the cheese is golden and bubbling. Allow the lasagna to rest for 10 minutes before slicing to help the layers set. This pause makes cutting much easier and the presentation neater.