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1
Preheat the oven to 375 degrees F.
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2
Rub the cut slices of the squash with 2 tablespoons of the olive oil and season with 1/2 teaspoon of the salt and 1/4 teaspoon of the white pepper.
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3
Set the squash, cut side down, on a baking sheet and roast until tender, 45 minutes to 1 hour.
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4
Remove from the oven.
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5
When cool enough to handle, scoop the flesh from the squash and place in a large bowl, discarding the skin.
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6
Mash into a chunky puree with a potato masher, then let cool, about 15 minutes.
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7
Add the remaining 1/4 cup of olive oil, 1/2 teaspoon of the salt, remaining 1/4 teaspoon white pepper, oregano, chopped sage and nutmeg, and work into the warm squash.
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8
Sprinkle the flour over the mixture and using your hands, work into a smooth, soft dough.
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9
Cover the dough with a damp kitchen towel and let rest for 30 to 45 minutes.
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10
Turn onto a lightly floured surface and divide into 4 equal portions.
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11
Roll each portion between your palms into a long rope, about 3/4-inch thick.
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12
If the rope won't hold together, return it to the bowl with the remaining dough and work in more flour, 1 teaspoon at a time, as needed.
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13
Cut each rope of dough into 3/4-inch long pieces.
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14
Press each piece against the tines of a floured fork, then drop into the lightly floured surface.
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15
(Gnocchi also can be placed in a single layer on a lightly floured baking sheet and refrigerated for several hours.
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16
Alternately, the gnocchi can be frozen for 1 hour then transferred to an airtight container and frozen for up to 1 month.)
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17
In a large pot, bring 4 quarts of water and the remaining 2 teaspoons of salt to a low boil.
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18
Add the gnocchi in batches and cook just until they float to the top, 1 1/2 to 2 minutes (or 3 minutes for frozen gnocchi.)
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19
For the Balsamic Brown Butter: In a medium saucepan, cook the butter over medium heat until brown bits form and it has a nutty aroma, about 3 minutes.
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20
Remove from the heat and add the shallots, balsamic vinegar, and sage.
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21
Stir well.
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22
Adjust seasoning, to taste.
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23
Remove the gnocchi from the water with a slotted spoon and dry on towels.
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24
Transfer to a large serving dish and gently toss to coat with the balsamic butter.
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25
Garnish with black pepper, parsley, chives, and shaved Parmesan.