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Heat the oven to 400F.
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Place the squash cut-side up on a baking sheet, and drizzle with a little olive oil (about 1/2-1 tsp). Place in the oven and bake for about 30-45 minutes until fork tender. Remove from the oven and allow to cool.
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Reduce the oven heat to 350F.
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Bring a pot of water to boil. Add the pasta, and cook according to the package instructions. Drain and set aside when done.
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While the water is boiling, place a medium-sized saucepan over medium-low heat. Add butter and melt.
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When butter is melted, whisk in the flour, and cook for an additional 15-30 seconds after it's completely incorporated.
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Slowly whisk in the milk so lumps do not form. Add a dash of salt and the nutmeg, and whisk often until the sauce thickens enough to coat a spoon.
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Turn the heat down to low, and stir in the Swiss and Gruyere cheeses.
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Scoop the flesh out of the cooled squash, and mash it using a fork or a potato masher. Stir half of the squash into the sauce.
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Add the pasta, sauce, and remaining squash to a baking dish (I used a 10x10in dish). Stir well to combine. Taste, and season with additional salt if needed.
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Top with the shredded mozzarella cheese.
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Cover with foil, and bake for 20 minutes. Then remove the foil, and bake for an additional 10 minutes.
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Serve!