This recipe is adapted from Jamie Oliver's cookbook "The Naked Chef Takes Off" (Hyperion, 2001).
Combine flours and mound on a clean work surface, forming a well in the center. Add eggs and yolks to well; beat until smooth with a fork. Gradually work flour into eggs. Continue to stir with fork until all of the flour has been incorporated.
Begin working dough with your hands to form a ball. Clean work surface of any loose bits of dough. Lightly flour surface; knead dough until smooth and elastic, about 10 minutes. Cover with plastic wrap, and let rest in refrigerator for at least 1 1/2 hours.
Divide dough into 4 pieces. Working with one piece at a time and keeping remaining pieces covered, flatten dough into a disc narrower than pasta-machine opening. Lightly dust dough with flour, and roll through the widest setting. Fold dough in half crosswise; pass through machine again. Repeat 4 or 5 times, running it through remaining settings until it is about 1/16 inch thick.
Cut pasta sheets to 12 inches long. Fold over twice, dusting both sides generously with semolina. Cut crosswise into 1-inch-wide slices. Gently shake pappardelle to separate lengths of pasta and remove excess flour. Pasta will keep fresh refrigerated for up to 12 hours.