Food processor:

Place flour and salt in the bowl of a large food processor and pulse to combine; add eggs, yolks, and olive oil. Process until crumbly. Add about 1/4 cup water while processing; continue to add water, 1 tablespoon at a time, just until dough forms a ball. Turn dough out onto a lightly floured surface, dust hands with flour, and knead, sprinkling with a little more flour if dough is sticky, until dough is smooth and elastic, at least five minutes and up to 10. Cover with a bowl and allow dough to rest for 30 to 45 minutes.

Stand mixer:

Place flour and salt in the mixing bowl of a stand mixer fitted with a dough hook; stir to combine. Add eggs, yolks, and olive oil; stir until crumbly. Add about 1/4 cup water while mixing; continue to add water, 1 tablespoon at a time, just until dough forms a ball. Set speed to medium-low and knead for 5 to 8 minutes, until dough is smooth and elastic. Turn out onto a lightly floured surface and knead several times; cover dough with a bowl and allow to rest 30 to 45 minutes.

If using a pasta machine, divide dough into 8 equal portions; cover unused portions while rolling out dough. Roll dough according to instructions and cut into desired shapes.

If rolling by hand, divide dough into 4 equal portions; cover unused portions while rolling out dough. Roll to desired thickness on a lightly floured surface and cut into desired shapes.

Lightly flour cut pasta to prevent it from sticking together; it may be dried and saved for later use, or cooked at once in a large pot of generously salted boiling water. Fresh pasta will cook quickly.