Add the flour and salt to the center of a large wooden board. Use your hands and make a well in the center of the mound. Whisk together the eggs and olive oil in a bowl and pour into the well. Use a fork to whisk the eggs into the flour, incorporating slowly into the rim of the flour until it is completely incorporated.
Once incorporated, knead the pasta for about 8 minutes, adding just a bit more flour if the board is sticky. If the dough feels too dry, add a drop of water as you go. The dough should feel elastic, smooth and a bit sticky. Shape the pasta dough into a ball and wrap in plastic wrap. Let rest for at least 30 minutes to 1 hour at room temperature to let the gluten relax so rolling will be easier.
Set your pasta machine to the widest setting. Divide the dough into 4 pieces. Roll each piece out from the widest setting to the thinnest. Hand cut the pasta into pappardelle.
Gather the strands together in your hands and shake loosely so they don't stick together. Toss with some semolina flour. Divide into portions on a sheet tray.
Bring a pot of salted water to boil. Boil the pasta until al dente and drain, about 3 minutes.
Recipe courtesy Gabriele Corcos and Debi Mazar, Extra Virgin, 2011