Preheat oven to 450°F. 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 for 10 minutes, then season with salt to taste. 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 rosemary (dried or fresh along with the sage if using). Heat milk mixture over low heat for 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-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 remaining sauce over pasta and sprinkle with 1/2 cup Parmesan. Make 1 more layer in the same manner, beginning and ending with pasta.
In a large mixing bowl beat cream with 1/2 teaspoon 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.
Spray foil with non-stick spray and cover dish with foil, tenting slightly to prevent foil from touching top layer. Bake in middle of oven for 30 minutes. Remove foil and bake lasagne 10 minutes more, or until top is bubbling and golden. Let lasagna stand for 5 minutes.
