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Step 1
In a food processor, pulse together flour and salt. Add eggs, yolks, and oil, and run the machine until the dough is beginning to hold together. If dough seems wet, add a little more flour. If dough is too crumbly, add a drizzle or two more olive oil.
Step 2
Dump dough and crumbs out onto a clean work surface knead together until very smooth. This will take a bit of muscle. Again, you can add a bit more flour, or a bit more oil, as needed. My batch of pasta needed more olive oil, in order to help with the kneading process. When the dough is smooth and supple, wrap it in plastic wrap, and let it rest at room temperature for one hour. This allows all the flour to become fully hydrated.
Step 3
Cut the dough disc into 4 portions. Work with one portion at a time, leaving the other portions covered in plastic wrap, or a dish towel, so as to not dry out.
Step 4
Attach the pasta roller attachment to your Kitchen Aid mixer, with the setting set at the thickest/widest level. Roll a portion of dough into a flat rectangle. Fold the sheet in thirds, like a letter, let it pass through the machine 2 more times at the widest setting.
Step 5
Move the dial to one click thinner, and pass the dough through two or three times before moving to the next thinnest setting. For pappardelle (1” wide) or fettuccine, stop rolling when the dough is 1 setting away from the thinnest setting on your roller.
Step 6
Place cut pasta on a flour dusted tray, sprinkle with flour, and cover with a dish towel, while you’re rolling and cutting the remaining portions of dough.
Step 7
Bring a large pot of water to a boil. Salt it well, and add fresh pasta strips. Boil for 1-3 minutes, depending on the thickness of your dough. (Sample a piece to be sure it’s cooked the way you like it.) Drain well. Serve with desired sauce, or simply some olive oil, salt, pepper, and Parmigiano Reggiano.