Preheat oven to 425 degrees. Toss squash, oil, and 1 teaspoon salt on a baking sheet. Season with pepper. Bake until light gold and tender, 25 to 30 minutes. Let cool.
Reduce oven temperature to 375 degrees. Combine ricotta, cream, yolks, mozzarella, and a pinch of nutmeg in a medium bowl. Season with salt.
Melt butter in a small saute pan over medium-high heat. As soon as it starts to sizzle, add sage, and cook until light gold and slightly crisp at edges, 3 to 4 minutes.
Place squash in a medium bowl, and mash 1/2 of it with the back of a wooden spoon, leaving the other 1/2 in whole pieces. Gently stir in sage-butter mixture and stock. Season with salt and pepper.
Spread 3/4 cup of ricotta mixture in a 9-cup 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 Parmesan over ricotta mixture.
Place baking dish on a rimmed baking sheet, and bake until cheese is golden and bubbling, 30 to 35 minutes. Let stand for 15 minutes before slicing and serving.