Butternut Squash Gnocchi with Sage Brown Butter

Preheat oven to 400°F. Cut squash lengthwise in half; discard seeds. Place squash halves, cut side up, on baking sheet and brush with oil. Roast until squash is very tender when pierced with skewer and browned in spots, about 1 1/2 hours. Cool slightly. Scoop flesh from squash into processor; puree until smooth. Transfer to medium saucepan; stir constantly over medium heat until juices evaporate and puree thickens, about 5 minutes. Cool. Measure 1 cup (packed) squash puree (reserve remaining squash for another use).

Meanwhile, cook potato in medium saucepan of boiling salted water until very tender, about 20 minutes. Drain. While potato is warm, press through potato ricer into medium bowl; cool completely. Measure 2 cups (loosely packed) riced potato (reserve remaining potato for another use).

Mix squash, potato, 1/2 cup Parmesan, egg, nutmeg, and salt in large bowl. Gradually add 1 3/4 cups flour, kneading gently into mixture in bowl until dough holds together and is almost smooth. If dough is very sticky, add more flour by tablespoonfuls. Turn dough out onto floured surface; knead gently but briefly just until smooth. Divide dough into 8 equal pieces.

Line 2 large rimmed baking sheets with parchment. Sprinkle parchment lightly with flour. 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. Working with 1 piece at a time, roll gnocchi along back of fork tines dipped in flour, making ridges on 1 side. Transfer gnocchi to baking sheets. Repeat with remaining dough. Cover loosely with plastic wrap and chill at least 1 hour. DO AHEAD Can be made 6 hours ahead. Keep chilled.

Working in 2 batches, cook gnocchi in large pot of boiling salted water until very tender, 15 to 17 minutes (gnocchi will float to surface but may come to surface before being fully cooked). Using slotted spoon, transfer gnocchi to same parchment-lined baking sheets. Cool. DO AHEAD Can be made 8 hours ahead. Cover loosely and chill.

Cook butter in heavy large skillet over medium heat just until golden, stirring often, 3 to 4 minutes. Add sage; stir 1 minute. Add gnocchi; cook until heated through and coated with butter, 5 to 7 minutes. Season with salt and pepper. Transfer to bowl. Sprinkle with 1/4 cup Parmesan. Serve with additional Parmesan.