1. Place the flour in a large bowl. Using the back of a measuring cup, create a large well in the center. Add the eggs, egg yolk, salt, and olive oil to the well, then, using a fork, whisk together without incorporating the flour. 
2. Continue whisking, adding the flour a little at a time until the flour is fully incorporated and the dough comes together. Using your hands, roll the dough into a ball and transfer to a clean work surface. Knead the dough for 7 to 8 minutes, or until the dough is smooth and elastic. Place the dough in a small bowl and cover with plastic wrap; rest at room temperature for about 30 minutes. 
3. Divide the dough into quarters. Roll each piece of dough as thin as possible (1/16-inch or 1 to 2 mm). If using a pasta machine, roll the dough pieces to ¼-inch thickness and feed each piece through twice, starting with the #1 setting. Sprinkle the dough sheets with flour and stack until ready to make noodles. 
4. Cut each sheet by hand into 1-inch thick strips. (Alternatively, run the dough sheets through the spaghetti or fettuccini attachment.) Arrange each noodle into a nest and place on a lightly floured sheet pan. 
5. If using immediately, bring a large pot of salted water to a boil. Add the pasta and cook until the pasta floats to the top, and is tender, 2 to 3 minutes. Drain and toss with sauce. To dry, hang the noodles over a wood dowel pasta dryer for 12 to 24 hours. Cook according to the same instructions.

Notes