2cupsegg noodlescooked according to the package directions
Preheat oven to 350 degrees F.
Heat the oil in a medium saucepan. Add the shallots and cook until soft. Add the flour and cook until browned and smooth, about 4 minutes. Stir in the milk. Bring to a boil, stirring constantly, and cook for 1 minute. Add the salt, pepper, and nutmeg and turn off the heat. Stir in the squash, Parmesan and half the cheddar and continue to whisk until smooth.
Add the noodles to a square baking dish and pour the sauce over top. Top with the remaining cheese and bake until cheese is melted, 15-20 minutes.