This is a wonderful and warming fall recipe that is filled with buttercup squash and cheese.
Preheat the oven to 350 degrees F.
Combine the squash, oil, cinnamon, fennel, salt, and pepper in a large bowl and toss well. Transfer the squash to a baking sheet. Bake in a 350 degrees until squash is soft, 18 to 20 minutes. Return the squash mixture to the bowl and stir in the thyme. Using a potato masher or fork, mash the squash well but leave some amount of chunkiness. Set aside.
Heat the milk on medium temperature with nutmeg, salt, and pepper until warm. In a separate small, thick-bottomed pan, melt the butter, being careful not to burn. Slowly whisk in the flour and sauté for a minute on low heat. Slowly whisk the warmed milk into the flour and butter mixture, making sure there are no lumps. Simmer on very low heat to ensure it does not burn while you are preparing to use it.
Cook the lasagna noodles according to the package instructions. Cool slightly.
In a 9 by 13-casserole dish, layer in béchamel sauce, then noodles, then the squash filling, and then the mozzarella cheese. Repeat the layers using remaining ingredients.
Pour the béchamel sauce on the top layer of noodles, spreading it to the edges. Sprinkle the Parmesan cheese evenly over the top. Cover with parchment paper and foil. Bake for 40 minutes in a 350 degree oven. Uncover and bake 5 minutes more. Let rest for 10 minutes and serve.