1. In a glass measuring cup, mix the whole eggs, egg yolks, olive oil and a pinch of salt. Put the flour in a food processor. Drizzle the egg mixture over the flour and process in long pulses until the dough is evenly moistened and forms small clumps, about 2 minutes. Transfer the dough to a work surface and knead until smooth and silky, about 2 minutes. Shape into a ball, wrap in plastic and let stand at room temperature for 15 minutes or refrigerate overnight.
2. Cut the dough into quarters; work with 1 piece at a time and keep the rest covered. Flatten the dough slightly and run it through successively narrower settings on a pasta machine until you reach the last setting. Trim the ends and cut the pasta sheet into 12-inch lengths. Drape the pasta sheets over a drying rack and let dry for 10 minutes. Repeat with the remaining dough.
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