Place the flour in a pile on a sturdy surface. Using your hands, make a well in the middle of the flour, then crack the eggs into the well and add the olive oil and salt.
With a fork, lightly whisk the eggs while gradually adding flour from the wall of the well into the center. When the mixture has a sticky consistency, begin to knead with your hands. Knead the dough for 15 minutes, adding a sprinkle of flour to the work surface as needed, to ensure the dough doesn't stick. Do not add a lot of flour at a time or your dough will be too tough.
Once the dough is smooth, tightly wrap it in plastic wrap and leave it to rest for 15 minutes.
Cut the dough into three even pieces. Then, take one piece and form it into a ball. Sprinkle some flour on your work surface and using a rolling pin, roll the dough as thin as possible in an oval shape and dust with a pinch of flour. Aim for 3mm in thickness.
Roll up the dough into a log. Cut down into 1.5 cm or 1 finger length.
Repeat the process for the other two balls of dough.
In a medium/large stockpot, bring salted water to a boil. Add in pasta and cook for 3 minutes, until cooked al dente. Serve with your preferred pasta sauce, or olive oil, parmesan, and basil.