Pour the flour out onto a work surface and make a well in the center. Add the whole eggs, egg yolks, the salt and olive oil.
Use a fork and start incorporating some of the flour into the liquids using a swirling motion. Once a paste is formed, use a dough scraper or your hands to work the ingredients into a solid, cohesive mass.
The dough will seem shaggy at first, but keep kneading it. After 4-5 minutes, it will come together into a smooth and silky dough.
Form the dough into a ball or disc, and wrap it tightly with plastic film. Let the pasta dough rest for 30 minutes. You can prepare it 24 hours ahead. Just place it in the refrigerator, and pull it a few hour before you plan to roll the dough out.