Cook pasta following directions on the box and drain well.
In a medium saucepan melt butter and add flour, salt and pepper.
Over medium-high heat whisk the butter mixture until it turns a golden brown. Slowly add milk to the pot while whisking.
Add 1 cup shredded cheddar cheese and nutmeg to the pot.
Bring to a boil, constantly whisking until thickened. About 5 minutes.
Place pasta in a baking dish.
Mix the butternut squash into the pasta well.
Pour sauce over pasta and mix until combined.
Cover with aluminum foil and bake for 25 minutes in a preheated 375-degree oven.
Remove from oven after 25 minutes and remove aluminum foil.
Sprinkle the remaining cheddar cheese and Parmesan cheese over the top.
Return to oven and bake 10 minutes or until the cheese has melted.