Add flour, eggs, yolks, olive oil, and salt to the bowl of a food processor. Process until dough comes around the blade of the processor, and continue to blend. Add additional flour, a half tablespoon at a time, until dough is smooth and still slightly tacky, about 1 minute. If dough is dry, add water, one teaspoon at a time.
Wrap dough in plastic wrap and let rest at least 1 hour at room temperature. If resting longer than 4 hours, transfer to refrigerator, where dough can rest up to 12 hours. Remove from the refrigerator 1 hour before rolling.
Unwrap dough and divide into 6 roughly equal portions. On a lightly floured surface, press into a rectangular shape with your palms, and then roll to a dimension of 9” x 12”. Dough should be very thin.
With the long side perpendicular to you, fold pasta sheet at 3″ intervals to form a flat roll. Use a sharp knife to cut into ½-inch wide noodles. Gently use unfurl the pasta, toss lightly with flour if necessary to keep from sticking, and place on a baking sheet, lightly covered with a clean kitchen towel, until ready to cook. Repeat with remaining dough.
To boil noodles, bring a large pot of generously salted water to a boil. Add noodles, gently stir, and cook, 2 minutes. Drain and serve with your favorite sauce.