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On the counter, or in a bowl, create a well with the flour. Sprinkle the salt over the flour.
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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 from the sides of the well into the center, mixing well with the eggs. Draw flour evenly from all sides.
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Working quickly, draw flour until a soft, loose dough forms.
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Continue to knead the dough, for 8 to 10 minutes until a firm, but not dry dough forms. Wrap in plastic wrap and let rest for 30 minutes.
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Fresh pasta cooks quickly, so start heating your water early, and melt the butter for the sage butter. Keep the butter on low heat until it's golden brown. While the butter is cooking, add the whole fresh sage leaves and cook until crisp. Remove from the butter and set aside for garnishing the plate. Add the minced sage; it will sizzle a bit. Remove the pan from the heat.
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After the dough has rested, divide into 4 even pieces. Set aside and cover 3 pieces while you work with the 4th. Lightly dredge your working piece in flour.
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Roll through the largest setting on your machine. Remove the dough, fold in thirds so the rounded ends meet in the center, turn the dough 90° (this will help square off the edges of the pasta sheet), and repeat the roll. Repeat again 4 times, for a total of 6 passes.
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After the 6th roll, dial the machine down to the next smallest setting. Roll the pasta through once, and dial down again. Only the first roll on the largest setting is done 6 times. Continue to roll thinner and thinner until you reach the 2nd smallest setting.
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Let the pasta sheets rest for 10 to 15 minutes. Be sure to check the pasta water. After the pasta has rested, lightly dust it with flour, cut the sheets into your 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 while you roll the rest of the sheets. After all 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 serve immediately. Refrigerate any leftovers.