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1
In the bowl of a standing mixer fitted with the paddle, mix the flour with 1 teaspoon of salt.
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2
Add the egg yolks and mix at medium speed until the dough is blended and resembles wet sand, about 1 1/2 minutes.
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3
Transfer to a work surface and knead until a firm dough forms.
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4
Cover with plastic wrap and let stand at room temperature for 30 minutes.
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5
Cut the pasta dough into 3 equal pieces and keep covered with plastic wrap.
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6
Working with one piece at a time, flatten the dough and run it through a pasta machine: Begin at the widest setting and work your way through consecutively narrower settings until you reach the thinnest one.
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7
Cut the sheet into 3 equal pieces.
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8
Run each piece through the spaghetti setting and transfer to a large rimmed baking sheet; toss the strands to keep them separate.
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9
Repeat with the remaining pasta dough.
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10
In a large skillet, melt the butter.
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11
Add the sage leaves and cook over moderate heat, turning once, until crisp, about 3 minutes.
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12
Season the sage with salt and pepper.
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13
Using a slotted spoon, transfer the sage to a plate; reserve the butter.
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14
In a large pot of boiling salted water, cook the pasta, stirring, until al dente, about 1 minute.
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15
Drain the pasta, reserving 1/4 cup of the pasta cooking water.
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16
Return the pasta to the pot, toss with the reserved butter and pasta cooking water and season with salt and pepper.
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17
Transfer to a large bowl and scatter the sage leaves and the 1/4 cup of cheese on top.
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18
Serve at once, passing additional cheese at the table.