Place the 00 flour on a clean work surface and create a large well in the center.
Add the whole eggs and egg yolks to the well and gently beat them together with a fork. Gradually draw flour from the inside edge of the well into the eggs. Continue until the mixture becomes thick.
Bring the mixture together with your hands to form a rough dough.
Knead for 8–10 minutes, until the dough is smooth, firm and pliable. If it remains excessively dry after several minutes of kneading, lightly dampen your fingertips and continue kneading.
Wrap the dough tightly and allow it to rest at room temperature for 30 minutes.
Divide the rested dough into four portions. Keep the unused dough covered.
Flatten one portion and pass it through the widest setting of a pasta machine. Fold and roll again as necessary until smooth. Continue rolling through progressively thinner settings until you have a thin but sturdy pasta sheet. Do not roll it paper-thin. ( See notes)
Cut the sheet into small rectangles. Working with one rectangle at a time, gently curve the two short sides upward to begin forming two shallow hollows.
Bring the center of the two long edges together and pinch firmly in the middle. Gently open and round the two sides with your fingertips to create two little boats joined at the center.
Place the shaped barchette on a tray lightly dusted with semolina and repeat with the remaining dough.
Bring a large pot of generously salted water to a gentle boil. Add the barchette and cook for approximately 3–5 minutes, tasting to determine doneness.
Transfer the pasta directly to your prepared sauce with a slotted spoon or spider. Toss gently and serve immediately.