5 cups shredded butternut squash (from about 1/2 peeled medium squash; shredded with the coarse grating attachment on a food processor or on a box grater)
1/4 cup thinly sliced fresh sage
1 pound fiorentini or other short curled pasta
Kosher salt
1/2 cup finely grated Parmesan or Grana Padano plus more
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