1. Pre-heat the oven to 375°.
2. If you are making fresh pasta, you could make the dough and have it resting while you prepare the filling and the sauce.

To make the butternut squash layer

1. In a shallow baking sheet toss the butternut squash with the 1 tablespoon of the olive oil and ½ teaspoon of the salt and the pepper.
2. Roast for 45 -60 minutes until the squash is tender and the edges are just starting to brown.
3. While the squash is roasting, fry the bacon in a large iron or non-stick fry pan. Cook the bacon until it is very crisp but not burned. Drain the bacon on paper towels, reserving the bacon grease. When cool crumble the bacon.
4. Heat the frying pan to medium heat. Sauté the chopped onion with 1 tablespoon of the bacon grease or 1 tablespoon of olive oil.
5. As the onion is cooking add ½ teaspoon of salt.
6. Continue to sauté until the edges are starting to brown and the onions have started to caramelize. It should take 30 minutes or so.
7. When the butternut squash is roasted with just the edges starting to brown remove from the oven and place in a medium bowl. Add the onion and 2/3 of the bacon. Let the mixture cool briefly.
8. Turn the oven down to 350°

At the same time you could be making the béchamel:

1. In a 4 quart saucepan bring the milk to a simmer with the parsley sprigs, nutmeg, onion slices, and black peppercorns. Let simmer for 5 minutes. Be careful not to let the milk boil over.
2. Strain the milk through a fine mesh strain into a heatproof measuring cup or bowl.
3. Clean out the saucepan.
4. Into the clean pan, melt the butter and add in the flour.
5. Stirring constantly, let the flour cook for a minute.
6. One ladle at a time, add in the hot milk mixture, stirring or constantly whisking to make a thick, smooth sauce. You can use a small whisk here; it helps if you have one. Let the sauce cook at a boil for 1 minute.
7. Ladle a cup or so of the hot liquid into the beaten eggs. Add the eggs back into the cooked sauce and let cook briefly stirring constantly.
8. Take off the heat and stir in the 1 cup of the parmesan cheese, season with salt and pepper. Set aside until you are ready to assemble.

When you are ready to assemble.

1. Bring a large pot of water to a boil and salt heavily.
2. Lightly grease a 13 X 9 baking dish with olive oil.
3. If you are making fresh pasta roll it out ending with #4 position in the rollers. Check my recipe for rich pasta dough for instructions. Cut into sheets that will fit the baking dish, you can cut them longer and fold over the excess at the end to seal in the lasagna like a package. When the water is boiling cook 2 sheets at a time of the fresh pasta. And layer as you go.
4. If you are using dried lasagna noodles, cook the pasta according to the package directions, drain let sit in cold water to stop the cooking process.
5. Stir into the cooled butternut squash and onion mixture about ½ cup of the Gruyere.
6. Layer enough pasta to cover the bottom of the baking dish. If you have cut the fresh pasta to do a package fold, let the noodles overhang by a couple of inches. let the excess stay around the edges until you have filled all the layers.
7. Ladle about 1/3 of the béchamel over the pasta and spread out to completely cover the bottom. Sprinkle about 1/3 of the remaining gruyere cheese, 1/3 of the grated parmesan, 1/3 of the walnuts, and a small sprinkling of the torn sage leaves (or sprinkle 1/3 of the dried).
8. Cover the béchamel layer with lasagna noodles.
9. Spread the Butternut squash filling completely over the pasta.
10. Cover the butternut squash layer with more lasagna noodles.
11. Ladle about 1/3 more of the béchamel sauce over the pasta. Spread out the sauce to completely cover the noodles. Sprinkle about 1/3 of the remaining gruyere cheese, 1/3 of the grated parmesan, 1/3 of the walnuts, and a small sprinkling of the torn sage leaves (or sprinkle 1/3 of the dried).
12. Cover with the remaining pasta. If you have fresh pasta overhanging, fold over the overhang like a package and then put one extra on top to seal it.
13. Ladle the remaining béchamel, spreading to completely cover the lasagna. Sprinkle the remaining walnuts, the reserved bacon, more of the sage, the remaining grated gruyere and the parmesan. Drizzle with a little extra olive oil if desired.
14. Bake the lasagna for 50-60 minutes, until the lasagna is golden brown and the cheese has melted. Let cool for 30 minutes before serving.