Prepare the squash and cheese filling. Prep time: About 1 hour. (Do this earlier in the day!)
Preheat oven to 425 degrees. Peel and seed the squash. Cut into 1-inch, bite size chunks.
Toss the pieces in a bowl with olive oil, 1 teaspoon salt, and some pepper. Spread out the pieces on a rimmed baking sheet, and bake 25-30 minutes.
While squash is baking, combine ricotta, cream, yolks, mozzarella and a pinch of nutmeg in a medium bowl. Season with salt. Cover and set aside in fridge.
Remove squash from oven. Let cool on pan.
Place squash in a medium bowl. Using the back of a large spoon, mash up most of the pieces, leaving a few large ones.
Melt the butter in a small sauté pan over medium-high heat. As soon as butter is sizzling, add the sage and cook 3-4 minutes.
Add sage mixture to squash along with chicken stock. Mix well. Cover and set aside in fridge.
Cook noodles and assemble lasagna. Prep time: About 1 hour.
Preheat oven to 375 degrees.
Cook lasagna noodles 1 minute less than what the package says.
In a 9-cup (or similar) baking dish, spread 3/4 cup ricotta mixture on bottom. 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 ricotta mixture over noodles and repeat once more (noodles, squash, noodles, ricotta).
Sprinkle parmesan over top and bake for 30-35 minutes.
Let stand a few minutes before serving.