Preheat the oven to 375°F (190°C). Lightly coat an approximately 11-by-8.5-inch deep baking dish with olive oil spray.
Place the butternut squash puree, ricotta, milk, 1/4 teaspoon salt, and nutmeg in a food processor. Blend until smooth and creamy.
Check the consistency of the squash filling. If it seems too thick to spread easily, blend in a little additional milk. Taste and add the remaining 1/8 teaspoon salt if needed.
For the spinach filling, combine the cooked and well-drained spinach with ricotta, 1 cup mozzarella, minced garlic, salt, and black pepper. Mix thoroughly and adjust the seasoning to taste.
Bring a large pot of water to a boil and cook the lasagna noodles according to the package directions. Drain and briefly rinse with cool water so they are easier to handle.
Spread one-third of the butternut squash mixture across the bottom of the prepared baking dish. Sprinkle lightly with mozzarella and cover with a single layer of lasagna noodles.
Spread half of the spinach mixture evenly over the noodles. Sprinkle lightly with mozzarella, then add another layer of noodles.
Spread another third of the squash filling over the pasta. Add a light layer of mozzarella followed by another layer of noodles.
Spread the remaining spinach filling over the noodles. Add a little mozzarella and cover with the final layer of pasta.
Finish your Butternut Squash and Spinach Lasagna by spreading the remaining squash filling over the noodles.
Sprinkle the top generously with Parmesan and the remaining mozzarella. Finish with Italian seasoning, paprika, and dried basil.
Cover the baking dish with foil and bake for 30 minutes.
Carefully remove the foil and continue baking uncovered for approximately 10 minutes, or until the cheese is melted and the edges are bubbling.
Let the lasagna rest for 10–15 minutes before slicing. This allows the layers to settle and makes serving much easier.