Add the flour, whole eggs, egg yolks and olive oil to the bowl of a food processor. Mix to combine until the dough comes together in a ball. It should be soft but shouldn't stick to your fingers.
Wrap the dough in plastic wrap or parchment paper, shaping it into a 6 inch log. Set is aside at room temperature for at least 1 hour or up to 4 hours.
Divide the dough into 6 parts.
On a lightly floured surface, take one piece of dough (leaving the rest of the dough wrapped in the plastic wrap, so it doesn't dry out) and with your fingers, pat the dough into about a 3 inch square.
Roll out the dough into a 6 inch wide and 20 inch long sheet of dough. You should be able to see the outline of your hand when you hold it up. Try to use as little flour as possible when rolling it out. The dough is very easy to work with and is soft and pliable, so you shouldn't have any problems.
Place the rolled out pasta sheet onto a lightly floured sheet of parchment, or your table surface, etc.
Repeat with the other 5 pieces of dough. Place each rolled out sheets of dough in one layer to dry for about 15 minutes. Don't put them on top of each other or they will stick together.
When the dough has dried for at least 15 minutes, roll in up starting with the short side, and use a sharp knife to cut across the rolled up pasta sheet, to get strands of pasta.
You can cut the pasta into thinner or thicker strands, or keep the pasta dough in sheets and use it for lasagna or make ravioli with it.
Lightly unfurl the pasta with your fingers.
You can freeze the pasta like this, by freezing it for about 20 minutes and then placing it into a ziptop bag or a sealed container.
To cook the pasta, bring a large pot of salted water to a boil.
When the water is boiling, add the pasta and cook on high heat for about 3 -5 minutes.
Drain the pasta, saving about 1/2 - 1 cup of the starchy water to thin out your sauce if you need to loosen the pasta a bit later.
At this point, you can use any sauce to the cooked pasta, gently tossing to evenly distribute the sauce. Add some of the reserved pasta water, to loosen the pasta a bit. Season with salt and pepper, if needed.
Garnish the pasta with fresh parsley or other fresh herbs. You can also garnish it with grated Parmesan cheese.