Pour the flour into a large, shallow bowl (or you can do this on the countertop). Make a well in the center. Add the egg yolks, water, olive oil, and a pinch of salt to the well. Use a fork to whisk the yolks, gradually pulling the flour into the liquid.
Continue to whisk until the flour absorbs most of the liquid. Use your hands to bring the dough into a shaggy ball, pressing all of the loose pieces together (at this point, it will seem like the dough is too dry, but it will continue to absorb in the next step).
Turn the dough out onto a clean surface. Knead the dough for about 5 minutes, or until smooth. Shape the dough into a ball and wrap it in plastic wrap. Let the dough sit at room temperature for 30 minutes.
Cut the dough into 4 pieces. Working with 1 piece at a time (keeping the rest covered), lightly dust both sides and then use a rolling pin to flatten it. Run the dough through a pasta roller on setting #1. Fold the dough in a tri-fold and run it through again.
Continue to run it through the pasta roller, working from setting #1 to setting #5. Place the rolled sheets on a floured surface and keep them covered. Repeat with the remaining pieces of dough.
Gently fold the sheets of dough and then cut them into ½” pieces, creating long strands of pasta. Separate the strands of pasta. Cook in boiling, salted water for about 3 minutes.
If you’d like to make the dough ahead of time, you can refrigerate it (after step 3) for up to 3 days and then pull it to room temperature for about 45 minutes before rolling.