Preheat oven to 400 degrees. Drizzle butternut squash halves with oil, and season with salt and pepper. Roast squashes, cut sides down, on a rimmed baking sheet until tender and browned, for about 45 minutes to 1 hour. Let cool. Scoop soft, roasted flesh from skins, and mash together by hand with a fork. Set aside.
Cook the lasagna noodles according to package directions. Drain and set aside, drizzling olive oil in between each lasagna noodle so as not to stick together.
Reduce the oven temperature to 375 degrees. In a large mixing bowl, combine the ricotta, heavy cream, egg yolks, mozzarella, 1 cup of the parmesan and a pinch of nutmeg. Mix together and season with salt. Set aside.
Melt the butter in a small saute pan over medium-high heat. As soon as it starts to sizzle, add the fresh sage, and cook until light gold and crisp at edges, 3 to 4 minutes. Remove the crispy sage leaves and set aside (do not discard). Mix in the roasted butternut squash and begin to assemble your lasagna.
To assemble the lasagna: Spread 3/4 cup of the ricotta mixture in your baking dish. Top with a layer of noodles. Spread 1/2 of the butternut squash mixture over noodles. Top with a layer of noodles. Spread 1 cup of ricotta mixture over noodles. Repeat layering once more (noodles, squash, noodles, ricotta). Sprinkle remaining cup of Parmesan (+ more if needed) over the ricotta mixture.
Place your baking dish on a rimmed baking sheet, and bake until the cheese is golden and bubbling, for about 30 to 35 minutes. Remove from the oven and crumble the crispy sage leaves on top. Let stand for 15 minutes before slicing and serving. Enjoy!