Cover the flesh of the squash with the olive oil and roast in a 425 degree F oven until very tender, 45 minutes to an hour. Allow to cool enough to remove the skin and mash the flesh. This can be done ahead of time and stored in the refrigerator until ready to use.
Cook and drain pasta. Set aside.
In a heavy bottom skillet, melt 2 tablespoons of the butter. Add onion and about 8 of the thinly sliced sage leaves. Start out with the heat on high and gradually reduce as the onions cook to allow them to brown without burning. A few minutes before they're done, add half of the garlic, stir, and allow to cook to golden brown.
Meanwhile, in a separate sauce pot, melt another 2 tablespoons of butter with the flour. Allow to cook over medium heat until golden brown and fragrant. Whisk in the milk and add the nutmeg. Continue to mix until the mixture bubbles and forms a gravy. Remove from heat and stir in the shredded cheddar and the mashed squash along with 1 teaspoon of salt.
Add the cooked pasta as well as the squash cheese sauce to the onion mixture and stir well to combine.
Melt the remaining 4 tablespoons of butter and combine with the bread crumbs and the remaining sage, garlic, and salt. Sprinkle crumb mixture on top of the pasta mixture.
Cook in 400 degree F oven until golden brown and bubbly, about 20 minutes.