Place the flour on a dry, clean work surface and form it into a mound. Create a large shallow well in the middle, making sure the walls are high enough to prevent the eggs from escaping. Add the eggs, yolks and olive oil to the well.
With a fork, beat the eggs; be careful not to disturb the walls of the flour. Once the eggs are well beaten, begin to incorporate the flour walls into the egg mixture. Continue incorporating the flour with the eggs with your fork until you have a shaggy, solid mass.
At this point, using your hands, start folding and forming the dough, incorporating the rest of the flour until you have a stiff, solid mass (removing any dry clumps of flour). Knead the dough. Drive the palms of your hand into the dough, pushing the dough forward. Continue, rotating the dough and folding the dough over its self, which helps to incorporate air pockets into the dough. Repeat until the dough is firm and bouncy and has a smooth, silken texture, about 10 minutes.
Wrap the dough in plastic and let rest 30 minutes.