Mound 3 1/2 cups of the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add the eggs and olive oil. Using a fork, beat together the eggs and oil and begin to incorporate the flour, starting with the inner rim of the well. As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape.
The dough will come together when half of the flour is incorporated. At this point, start kneading the dough with both hands, using the palms of your hands.
Once there is a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky.
Wrap the dough in plastic and allow to rest for 30 minutes at room temperature.