Place the 2 cups of all-purpose flour, 3 whole eggs, and 1 egg yolk directly into your blender. Pulse the mixture in short bursts. Do not let the blender run continuously for a long time, as you do not want to overheat the ingredients. Keep using intermittent pulses until the eggs and flour combine and a cohesive dough begins to form.
Pour the dough out onto a clean, flat work surface. If the mixture feels a bit sticky, dust a small amount of extra flour onto the surface. Knead the dough vigorously by hand. Continue pressing and folding until the texture transforms from shaggy to completely smooth, elastic, and satiny.
Tightly wrap the smooth ball of dough in plastic wrap. Place it into the refrigerator to rest for at least 30 minutes. This step relaxes the gluten, which makes the dough significantly easier to roll out later without it snapping back.
Remove the rested dough from the refrigerator and place it onto a lightly floured surface. Cut the dough evenly into four quarters. Roll each quarter into a small ball, then use the palm of your hand to press it down as flat as possible before introducing it to the machine.
Set your pasta maker to Level 0 (the widest setting). Pass one of your flattened dough portions through the rollers. Fold the resulting sheet in half, dust it lightly with flour, and run it through level 0 again. Repeat this folding and rolling process a few times until a clean uniform rectangle shape is nicely formed.
Gradually roll your pasta sheet through the machine, dropping down one level at a time (from Level 1 up through Level 8). Make sure to dust the sheet lightly with flour if it starts to feel sticky at any point. Stopping at Level 8 yields the ideal, silky thickness for ribbon pasta. Repeat this entire rolling process for the remaining three quarters of dough.
Take your long pasta sheets and cut them in half crosswise to create a manageable length for eating. Slice the sheets lengthwise into uniform, thin strands using a pizza cutter, a sharp knife, or your machine's cutting attachment.
Generously dust the freshly cut ribbon strands with flour. Gently toss them with your fingers so the flour coats each strand completely, preventing them from sticking together before they hit the cooking pot.
