Toss squash with oil in bowl. Season with salt. Roast squash in shallow, oiled pans at 450 degrees until tender & golden.
In a large pot, boil lasagna sheets. When done, drain, rinse with cold water, and set aside.
In large saucepan, cook garlic in butter until soft. Stir in flour and cook the roux 3 minutes. Whisk in milk slowly, stirring till smooth. Simmer 10 minutes, stirring. Add squash. Season with salt, pepper, paprika. (You can make the sauce ahead of time.)
Reduce oven to 375 degrees. Butter a 13 x 9" baking dish. Pour in 1 cup of the sauce. Cover with 3 sheets lasagna. Spread half of the remaining sauce over this, sprinkle with 1/2 cup parmesan cheese. Make 1 more layer of pasta, sauce, cheese, and end with another pasta layer.
Beat cream with salt to hold soft peaks. Cover pasta with cream. Sprinkle with remaining 1/2 cup of parmesan. Cover tightly with foil. Bake 30 mins. Uncover, bake 10 mins. Let stand 5 mins before serving. Sprinkle chopped parsely over top.