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.
Because fresh pasta is more supple than dried, the uncovered edge of store-bought noodles will crisp more readily than the fresh version.