Mound 3 cups of flour on a clean counter or cutting board. Make a large well in the middle of the flour and add the eggs, olive oil, and salt. Using a fork, beat the eggs. Using your finger tips begin to incorporate the flour a little bit at a time, pulling flour from the rim of the well into the egg mixture.
As the well grows outward due to adding more flour to the center, keep pushing up flour from the base to maintain the shape of the well. The dough will come together with approximately half of the flour used. Start kneading the dough, pushing with the palm of your hands, rolling the dough back onto itself, and then pushing with your palms again, adding flour as needed. Repeat this process until the dough is smooth and elastic – about ten minutes.
Form the dough into a ball and wrap with plastic wrap. Allow the dough to rest for 30 minutes at room temperature.