3 tablespoons vegetable oil
3 pounds butternut squash, quartered, seeded, peeled, and cut into 1/2-inch dice (approximately 9.5 cups) Salt, to taste
4 cups milk (2% or whole)
2 tablespoons dried rosemary, crumbled (or a few fresh sprigs)
Sage, a few fresh sprigs (optional)
1 tablespoon minced garlic
1/2 stick (1/4 cup) unsalted butter
4 tablespoons all-purpose flour
9 (7-inch x 3.5-inch) sheets dry no-boil lasagna
1 1/3-cups freshly grated Parmesan
1 cup heavy cream
1. Preheat oven to 450°F and oil 2 large shallow baking pans with a tablespoon of oil each.
2. Spread squash on each sheet pan and toss with oil until coated well. Add additional tablespoon of oil if necessary. Roast squash in oven for 10 minutes and then season with salt. Stir squash and roast 10 to 15 minutes more, or until tender and beginning to turn golden.
3. While squash is roasting, bring milk to a simmer in a saucepan with rosemary and the sage if using. Heat milk mixture over low heat for about 10 minutes and pour through a sieve into a large pitcher or measuring cup.
4. In a large heavy saucepan cook garlic in butter over moderately low heat, stirring often until softened. Stir in flour and cook roux, stirring, for about 3 minutes. Remove pan from heat and whisk in the milk mixture in a stream until smooth. Return pan to heat and simmer sauce, whisking occasionally, for 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.
5. Reduce oven temperature to 375°F.
6. Butter a 13-inch x 9-inch x 2-inch baking dish. Pour 1 cup sauce into baking dish (sauce will not cover bottom completely) and cover with 3 lasagna sheets, making sure they do not touch each other. Spread half of the remaining sauce over pasta and sprinkle with 1/2 cup Parmesan. Make 1 more layer in the same manner, beginning and ending with pasta.
7. In a bowl with an electric mixer (or with a whisk) beat cream with salt until it holds soft peaks, then 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 the middle of oven for 30 minutes. Remove foil and bake lasagna for 10 more minutes, or until top is bubbling and golden.
8. Let lasagna stand for 5 minutes and serve.