1 medium butternut squash (about 2 1/2 pounds)
1 tablespoon olive oil
1 1/2 pounds sweet Italian sausage, casings removed
1 pound fresh spinach
1 pound dry lasagna noodles
1/2 cup (4 ounces) unsalted butter
1/2 cup all-purpose flour
6 cups whole milk
1/2 teaspoon freshly grated nutmeg
1/2 teaspoon salt
1 pound fresh mozzarella, torn into bite-size pieces
1/2 cup grated Parmigiano Reggiano
Butter, to grease the dish
Cook the butternut squash: Preheat the oven to 400°F. Peel the squash and cut the neck into round slices, 1/4-inch thick. When you get to the bottom of the squash, slice it in half, remove the seeds and pulp, and slice each half into 1/4-inch thick half moons. Place the slices on a large baking sheet, drizzle with the olive oil, and toss to evenly coat. Spread the squash in an even layer and roast until tender, about 20 minutes, flipping halfway through.
Cook the sausage: Place a large skillet over medium-high heat and, once hot, add the sausage to the pan. Once it begins to brown, use a wooden spoon to break the sausage into small pieces. Continue to cook, stirring occasionally, until uniformly browned and cooked through.
Cook the noodles: While cooking the sausage, bring a large pot of salted water to a boil over high heat. Stir in the noodles and cook until al dente. Remove using tongs and place in a single layer on clean kitchen towels.
Blanch the spinach: Fill a bowl with ice and cold water, and place it near the stove. Bring the pasta water back to a boil and add the spinach. Cook until wilted and bright green. Scoop the spinach from the water with a slotted spoon and transfer to the ice water bath. Once cool, drain the spinach, squeeze it of excess water, and then chop finely.
Make the bechamel: In a deep saucepan or medium pot, melt the butter over medium heat. Stir in the flour and cook for 2 minutes. Slowly pour in the milk, whisking to combine smoothly. Add the nutmeg and salt and continue cooking, stirring often, until thick enough to coat the back of a spoon.
Assemble and cook the lasagna: Heat the oven to 350°F.
Grease the bottom of a 2-quart baking dish. Add a single layer of noodles, and spread about a fourth of the bechamel over top. Top with half the spinach and a third of the mozzarella. Add another layer of noodles, a fourth of the bechamel, half the sausage, half the squash, and another third of the mozzarella. Add a third layer of noodles, a fourth of the bechamel, the second half of the spinach, the second half of the sausage, the second half of the squash, and the final third of the mozzarella. Add one more layer of