Preheat the oven to 375 degrees F. Butter a 9" x 13" baking dish and set aside.
Empty the two cans of butternut squash into a mixing bowl and season with salt and pepper.
Grate all the cheeses. Mix together the mozzarella and fontina. Keep the parmesan separate.
Make the bechamel sauce. In a large skillet, melt the butter over medium heat. Add the flour and mix together for about one minute.
Gradually whisk in the milk so no lumps remain. Bring to a boil, then simmer for about 5 minutes until the mixture thickens and will coat the back of a spoon. Whisk in the nutmeg and sage, season with salt and pepper.
Add ¾ cup of the milk mixture to the bottom of the baking dish. Place three of the no-boil noodles on top of the sauce. Spread ⅓ of the butternut squash on top of the noodles. Top with ½ cup of the mozz/fontina cheese mixture. Drizzle with ½ cup of the bechamel sauce.
Repeat the layers in this way using the same measurements: noodles, squash, cheese, bechamel, noodles, squash, cheese, bechamel.
Add the final three noodles, then top with all remaining bechamel sauce and all remaining mozzarella/fontina mixture.
Cover with foil and bake for about 45 minutes, until lasagna is bubbling and cheese is melted.
While the lasagna is baking, heat 1 tablespoon of olive oil in a small skillet over medium heat. Fry sage leaves until they curl slightly and are fragrant, about 30 seconds. Allow to drain on a dry paper towel.
Remove foil, top with the shredded parmesan cheese and bake for about 15 minutes until the cheese is golden brown. Remove from the oven and allow to stand 15 minutes before serving.
Top with the sage leaves and serve.