Step 1

Preheat oven to 450°F. Spread the squash onto 1 extra-large sheet pan or 2 standard-sized sheet pans. Toss with 2 tablespoons of oil if using the large pan or 1 tablespoon each if using the smaller sheet pans. Season with salt and toss to coat. Transfer to the oven and cook for about 30 minutes, tossing halfway,  until the squash is tender and beginning to turn golden.

Step 2

While squash is roasting, in a saucepan bring milk to a simmer with the rosemary and sage sprigs. Heat milk mixture over low heat for 10 minutes and pour through a sieve into a large pitcher or measuring cup.

Step 3

In a large heavy saucepan cook garlic in butter over moderately low heat, stirring, until softened. Stir in flour and cook the roux, stirring often, for about 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 the squash and salt and pepper to taste. Sauce may be made 3 days ahead and chilled, its surface covered with plastic wrap.

Step 4

Reduce temperature to 375°F and butter a 9×13-inch baking dish. UPDATE: Because sometimes no-boil noodles do not expand as well as expected, you can quickly soak them in hot water. If you’ve never had trouble with your no-boil noodles, don’t worry about this step. If you have, I think you’ll find this step makes a difference: Bring a small pot of water to a boil or fill a teapot with water and bring it to a boil. Pour the water into a small vessel such as a 9-inch baking. When you are ready to assemble, dunk three of the sheets into the hot water and let soak. Begin the assembly:

Step 5

Pour 1 cup sauce into baking dish (sauce will not cover the bottom completely) and cover with 3 lasagna sheets, making sure they do not touch each other – use tongs to extract the noodles from the hot water. After you transfer the three noodles to the baking dish, soak three more sheets of noodles. Spread half of the remaining sauce (it’s about 2 cups) over the noodles and sprinkle with 1/2 cup parmesan. Top with three more noodles; then soak the final three noodles in the hot water bath. Spread the remaining sauce mixture over the noodles and top with 1/2 cup parmesan. Top with the final layer of noodles.

Step 6

In a bowl with an electric mixer (or by hand) beat cream with salt until it holds soft peaks and spread evenly over the 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 lasagna 10 to 20 minutes more, or until top is bubbling and golden. Let lasagna stand 5 minutes before cutting and serving.