Preheat oven to 425 degrees, and start cooking the lasagna noodles now if not done already. 

In a  bowl, combine the squash cubes, oil and salt. mix to coat then arrange on a baking sheet. Bake until caramelized, about 25-30 minutes. Set aside and allow to cool. Reduce oven temperature to 375 degrees.

Combine ricotta, milk, egg yolks, mozzarella (reserve some for the topping unless you want to add more to the amount, which is suggested), and 1 tsp of the salt in a medium-sized bowl.

Melt the butter in a small pan on the stove, over medium-high heat. As soon as it starts to sizzle, add the fresh sage and cook until golden and crisp at the edges, about 3-4 minutes.

Place the 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 vegetable stock. Season with pepper at this time if you wish. 

Spread 3/4 cup of ricotta mixture into a baking dish. Top with a layer of noodles. The spread 1/2 of the butternut squash mixture over noodles. Top with a layer of noodles. Spread more ricotta mixture over noodles. Repeat layering once more if you can (noodles, squash, noodles, ricotta). 

Sprinkle additional mozzarella over ricotta mixture.

Place baking dish on a rimmed baking sheet to catch excess, and bake until cheese is golden and bubbling, about 30-35 minutes

Let stand for 15 minutes then slice and serve. Enjoy!