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Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. Place the flour on the counter or in a large, shallow bowl, then create a large well in the center. Sprinkle the salt over the flour. (For instructions on how to make the dough in a food processor, see "tips," below.)
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Crack the eggs directly into the well. Scramble them with your fingers or a fork.
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Draw flour evenly from all of the sides of the well into the center, mixing it into the eggs. Continue to draw flour until a soft, loose dough forms.
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Knead the dough until a firm but not dry dough forms, 8 to 10 minutes. Wrap in plastic wrap and let rest for 30 minutes.
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While the dough rests, bring a large pot of heavily salted water to a boil and prepare the sauce. (Fresh pasta cooks quickly, so it's important to have the sauce ready as soon as it's done cooking.) In a large saucepan, melt the butter for the sauce. If you'd like to have whole fresh sage leaves for garnish, add them to the butter and cook, stirring occasionally, until the butter is golden brown and the sage leaves are crisp. Remove the sage leaves from the butter and set aside for garnishing. Add the minced sage; it will sizzle a bit. Remove the pan from the heat and set aside.
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After the dough has rested, divide into four even pieces. Set aside and cover three pieces while you work with the fourth. Lightly dredge your working piece in flour.
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Roll the dough through a pasta machine once on the largest setting. Fold the dough in thirds like a letter (this helps it become a rectangular shape) before rolling it a second time on the largest setting.
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Adjust the pasta machine to the next increment and pass the dough through. Continue adjusting the setting and rolling the dough through the machine until you’ve used setting #7 on a standard pasta roller (0.8 mm thick).
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Generously dust the pasta sheets with flour, cut to desired length, and run each sheet through the cutting blades of the pasta machine.
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Gently separate the noodles, and loosely pile the pasta on a baking sheet or clean surface while you roll the rest of the sheets. After all the sheets are cut, add the pasta to the salted boiling water. Cook for 2 to 3 minutes.
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Drain the pasta, leaving a couple of tablespoons of the cooking water in the pot. Stir in the sizzled sage butter and season to taste with salt and pepper. Serve immediately. Refrigerate any leftovers.