2 cups all-purpose flour
1 large egg
4 tablespoons extra-virgin olive oil
Ice water as needed
To mix the dough: Put the flour in the bowl of the food processor and process for a few seconds to aerate. Mix with a fork the whole eggs and egg yolks, olive oil; and 1/4 cup ice water in a small bowl until just blended.
With the machine running pour the liquids quickly into the feed tube on top of the flour. After 20 seconds, most of the dough should clump up on the blade. Process for another 15 seconds or so-no more than 40 seconds total. (If the dough does not gather on the blade and process easily, it is too wet or too dry. Feel the dough, then work in either more flour or ice water, in small amounts, using the machine or kneading by hand.)
Turn the dough out on a lightly floured surface and knead it by hand for a minute until it's smooth, soft and stretchy. Press it into a disk, wrap well in plastic wrap and let it rest at room temperature for a half hour.
To roll out the dough in a pasta machine: Cut the pound of dough into 4 equal pieces. Work with one at a time and keep the others covered. Run the first piece of dough through the rollers at the widest setting several times to develop strength and smoothness. Repeat with all the pieces. Re-set the machine to a narrower setting and run the first piece through extending it into a rectangular strip. Let the rollers move the dough and catch it in your hand as it comes out. Roll it again to stretch and widen it. Lightly flour and cover the strip, then stretch the other pieces.
Roll and stretch all the pieces at progressively narrower settings, until they spread as wide as the rollers (usually about 5-inches) and stretch to 20-inches or longer. Cut the 4 long pasta strips in half crosswise, giving you 8 sheets, each about a foot long and 5-inches wide. Lay these flat on the trays in layers, lightly floured, separated and covered by towels.
To cut pappardelle: Lay out a rolled sheet on the floured board; dust the top with flour. Starting at one of the short ends, fold the sheet over on itself in thirds or quarters, creating a small rectangle with 3 or 4 layers of pasta.
With a sharp knife, cut cleanly through the folded dough crosswise, in 2-inch wide strips. Separate and unfold the strips, shaking them into long noodles. Sprinkle them liberally with flour so they don't stick together. Fold, cut and unfurl all the rolled pasta sheets this way, and spread them out on a floured tray. Leave them uncovered, to air-dry at room temperature, until ready to cook.