On a large, clean work surface, pour flour in a mound. Make a well in the center. Pour whole eggs, egg yolks, and salt into well and, using a fork, beat thoroughly. When combined, gradually incorporate flour into the eggs until a wet, sticky dough has formed.
Using a bench scraper, scrape excess dough from fork and fingers. Begin to fold additional flour into the dough with the bench knife, turning the dough roughly 45 degrees each time, until dough feels firm and dry, and can form a ball, 2 to 5 minutes.
Knead the ball until dough develops a smooth, elastic texture, adjusting the liquid if needed. Wrap ball of dough tightly in plastic wrap and rest on countertop for 30 minutes.
Meanwhile, place a sheet of parchment on a baking sheet and and dust lightly with flour. Unwrap rested dough and cut into quarters. Set one quarter on work surface and re-wrap remaining dough. With a rolling pin, flatten the quarter of dough into an oblong shape about 1/2 inch thick.
Set pasta maker to widest setting and pass dough once or twice. Place dough on a lightly floured work surface. Fold both ends in so that they meet at the center of the dough, and then fold the dough in half where the end points meet, trying not to incorporate too much air into the folds. Using rolling pin, flatten dough to 1/2-inch thick. Pass through the roller another couple of times.
Narrow the setting by 1 notch and repeat the last step. Continue passing the dough through the rollers, reducing the thickness by 1 setting each time until it reaches the desired thickness. It should now be very delicate and almost see through.
Place rolled dough onto a work surface lightly dusted with flour, folding the dough over. Sprinkle with flour between folds to prevent sticking. Fold a few times, then use a chefs knife to slice into your desired thickness. Shake the pasta ribbons loose and toss with flour. Shape into a nest and place on flour lined baking sheet, then continue with the rest of the dough.