Slightly adapted from Gourmet

3 pounds butternut squash, quartered, seeded, peeled, and cut into 1/2-inch dice (about 8 to 9 cups of cubed squash)

3 tablespoons grapeseed or olive oil

4 cups milk, 2% or whole

a few sprigs fresh rosemary and sage

1 tablespoon minced garlic

4 tablespoons unsalted butter

4 tablespoons all-purpose flour

nine 7- by 3 1/2-inch sheets dry no-boil lasagne pasta (I use Barilla brand)

1 1/3 cups freshly grated Parmesan

1 cup heavy cream

1/2 teaspoon salt

Preheat oven to 450°F and oil 2 large shallow baking pans with a tablespoon of oil each.
Spread squash on each sheet pan and toss with oil until coated well. Add additional tablespoon of oil if necessary. Roast squash in oven 10 minutes, then season with salt. Stir squash and roast 10 to 15 minutes more, or until tender and beginning to turn golden.
While squash is roasting, in a saucepan bring milk to a simmer with the rosemary and sage sprigs. Heat milk mixture over low heat 10 minutes and pour through a sieve into a large pitcher or measuring cup.
In a large heavy saucepan cook garlic in butter over moderately low heat, stirring, until softened. Stir in flour and cook roux, stirring, 3 minutes. Remove pan from heat and whisk in milk mixture in a stream until smooth. Return pan to heat and simmer sauce, whisking occasionally, about 10 minutes, or until thick. Stir in squash and salt and pepper to taste. Sauce may be made 3 days ahead and chilled, its surface covered with plastic wrap.
Reduce temperature to 375°F and butter a 13 by 9 by 2 inch baking dish.
Pour 1 cup sauce into baking dish (sauce will not cover bottom completely) and cover with 3 lasagne sheets, making sure they do not touch each other. Spread half of remaining sauce over pasta and sprinkle with 1/2 cup Parmesan. Make 1 more layer in same manner, beginning and ending with pasta.
In a bowl with an electric mixer (or not) beat cream with salt until it holds soft peaks and spread evenly over top pasta layer, making sure pasta is completely covered. Sprinkle remaining 1/3 cup Parmesan over cream. Cover dish tightly with foil, tenting slightly to prevent foil from touching top layer, and bake in middle of oven 30 minutes. Remove foil and bake lasagne 10 minutes more, or until top is bubbling and golden. Let lasagne stand 5 minutes.