Preheat your oven to 400°F. Peel the butternut squash and slice the neck into 1/4-inch rounds. Halve the bottom part of the squash, scoop out the seeds, and slice into 1/4-inch half-moons. Toss the squash in olive oil, spread on a baking sheet, and roast for about 20 minutes, flipping halfway through, until soft.

In a large skillet over medium heat, cook the sausage. Break it up into pieces and stir occasionally until fully browned and cooked through.

Boil a large pot of salted water. Add lasagna noodles and cook until just tender (al dente). Remove noodles from the water and lay them flat on clean towels to prevent sticking.

Reuse the pasta water to blanch the spinach. Boil the spinach briefly until wilted and bright green, then transfer it to a bowl of ice water. Drain, squeeze out excess water, and finely chop.

In a deep saucepan, melt the butter over medium heat. Stir in the flour, cooking for 2 minutes. Gradually whisk in the milk. Add nutmeg and salt, stirring until the sauce thickens to coat the back of a spoon.

Lower the oven temperature to 350°F. Butter a 2-quart baking dish. Start by layering lasagna noodles at the base. Spread a quarter of the béchamel over the noodles, then add half of the chopped spinach and a third of the mozzarella.

Continue layering with more noodles, a quarter of the béchamel, half the sausage, half the roasted squash, and another third of the mozzarella. Repeat the layering process one more time with the remaining ingredients.

For the top layer, add the final portion of noodles, the last of the béchamel sauce, and finish with grated Parmigiano Reggiano.

Bake for 30 minutes or until the lasagna is bubbling and the cheese has melted. Optionally, broil for a few minutes to get a golden-brown top. Let the lasagna cool for 15 minutes before slicing and serving.