Mound the flour in the center of a counter or large cutting board. Make a well in the middle of the flour 3 to 4 inches wide. Crack the eggs into the well and add the yolks and salt. Using a fork, break the yolks and begin to beat the eggs as if you were making scrambled eggs.
Continue stirring the eggs in large circles with the fork, slowly incorporating the flour from the inner edges of the well until the mixture becomes a thick mass and is difficult to stir, about 3 minutes. Using a bench scraper or rubber spatula, fold the loose flour from the edges into the thick mass, then knead until a smooth dough forms. Discard any excess flour.
Shape the dough into a flat disk, wrap tightly with plastic wrap and let rest at room temperature for 30 minutes. (The dough can be made 1 day ahead. Store it in the refrigerator tightly wrapped and let it come to room temperature before rolling.)
Secure the pasta attachment to a stand mixer or, if using a hand-crank machine, attach it to the counter. Set the machine to the widest setting. Unwrap the dough and cut it into 4 equal pieces. Wrap 3 of the pieces and set aside while you work with the remaining piece of dough.
Flatten the dough into a rectangle and lightly dust it with flour. Roll it through the pasta machine at the widest setting. Fold the dough in thirds like a letter and feed it through the pasta machine. Repeat the folding and feeding of the dough through the machine 2 more times. (Folding and rolling it in this manner helps strengthen and smooth the dough.)
Set the pasta machine to the next setting (one setting thinner than the widest). Flour the dough as needed and feed it through the machine. Repeat one more time.
Adjust the machine to the next thinnest setting and feed the dough through 2 times. Continue changing the setting and feeding the dough through 2 times for each setting until you have fed the dough through the second-to-last setting. The sheet of pasta should be thin enough so that you can see your hand through it.
To make pappardelle, cut the sheet crosswise into 10- to 12-inch-long pieces, then cut each piece with a chef’s knife into 1-inch-wide noodles. Lightly toss the noodles with a little flour on a baking sheet to prevent sticking. Cover with a dry kitchen towel while you repeat the process with the remaining dough.
To make hand-shaped fusilli, cut the sheet crosswise into 1/4-inch-wide strips. Wrap them around a thin dowel, skewer or chopstick, forming a corkscrew-like shape, then gently slide each one onto a baking sheet. Lightly toss the fusilli with a little flour to prevent sticking. Cover with a dry kitchen towel while you repeat the process with the remaining dough. (Making fusilli is great to do with kids as a group.)
Cook the noodles in a large pot of boiling salted water until al dente, 3 to 4 minutes.