Step 1

Preheat oven to 400°F.

Step 2

Cut squash lengthwise in half; discard seeds. Place squash halves, cut side up, on baking sheet and brush with oil.

Step 3

Roast until squash is very tender when pierced with skewer and browned in spots, about 1 hour.

Step 4

Let it cool slightly. Scoop flesh from the squash into a food processor and puree until smooth.

Step 5

Transfer the puree to a medium nonstick saucepan and stir constantly over medium heat until juices evaporate and puree thickens, about 15 minutes. When it’s done the squash’s consistency should resemble loose dough and thick enough to cling to an upended spoon.

Step 6

Measure 1 cup (packed) squash puree and let it cool. Reserve the remaining squash for another use.

Step 7

In a large mixing bowl, combine squash, flour, Parmesan, egg, egg yolk, nutmeg, and salt and mix with a spoon until the dough comes together. If the dough is very sticky, add more flour by one tablespoonful.

Step 8

Turn the dough out onto floured surface; knead gently but briefly just until smooth. Divide dough into 8 equal pieces, wrap in plastic, and refrigerate for 4 hours or overnight to firm up.

Step 9

Line 2 large rimmed baking sheets with parchment and sprinkle lightly with semolina flour.

Step 10

Working with 1 dough piece at a time, roll dough out on floured surface to about 1/2-inch-thick rope. Cut rope crosswise into 3/4-inch pieces.

Step 11

Working with 1 piece at a time, roll gnocchi along a gnocchi board.

Step 12

Transfer gnocchi to baking sheets. Repeat with remaining dough.

Step 13

Cover loosely with a kitchen towel and chill at least 1 hour in refrigerator.

Step 14

When ready to cook, bring a pot of salted water to a boil.

Step 15

Working in 4 batches, drop gnocchi in the pot and let them cook for 3-5 minutes until they float to the surface or become springy to touch.

Step 16

Using a slotted spoon, transfer gnocchi to a large plate.

Step 17

Cook butter in heavy large skillet over medium heat just until golden, stirring often, about 4-5 minutes.

Step 18

Add sage and cook for 2 minutes until crips. Add gnocchi and cook until heated through and coated with butter, about 5 minutes. Season with salt and pepper to taste.

Step 19

Transfer gnocchi to warmed plates. Serve with additional Parmesan, toasted walnuts, and garnish with crispy sage.