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1
Pulse flour and salt in a food processor once or twice.
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2
Add the eggs and yolks, and turn the machine on.
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3
Process just until a ball begins to form, about 30 seconds.
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4
Add a few drops of water if the dough is dry and grainy; add a tablespoon of flour if the dough sticks to the side of the bowl.
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5
Turn the dough out of the food processor, sprinkle it with a little flour, cover it with plastic or a cloth, and let it rest for about 30 minutes.
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6
(At this point, you may refrigerate the dough, wrapped in plastic, until youre ready to roll it out, for up to 24 hours.)
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7
Meanwhile, in a food processor or blender, combine the basil with a pinch of salt, the garlic and about half the oil.
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8
Process, stopping to scrape down the sides of the container if necessary, and adding the rest of the oil gradually.
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9
Add the nuts and cheese, and pulse a few times.
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10
The pesto should be well combined but still chunky.
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11
Bring a large pot of water to a boil and salt it.
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12
Divide the dough in half.
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13
Turn one half of the dough onto a lightly floured surface and roll it into a large rectangle no thicker than 1/4 inch and ideally closer to 1/8 inch, adding additional flour sparingly as necessary.
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14
Repeat with the rest of the dough.
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15
Cut into squares no larger than 4 inches across.
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16
Drop the squares into the water and cook until tender, 2 to 3 minutes.
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17
Drain, reserving a little of the cooking water.
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18
Toss the handkerchiefs with the pesto, some salt and pepper, and a spoonful of cooking water, if necessary, to thin the pesto.
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19
Serve immediately, garnished with Parmesan.
