Make the dough. Sift both flours together on a large work surface and make a well in the center. Place the eggs, olive oil and a pinch of salt in a bowl, then pour into the well; with a fork, break up the eggs, then gradually mix the wet ingredients into the flour mixture just until combined.
Knead by hand. Gather the dough into 2 equal-size balls; flour the surface. To knead each piece, push the dough away from you with the heel of your hand, fold the dough over itself and turn it counterclockwise. Continue pushing, folding and turning until the dough is smooth and elastic, 4 to 5 minutes.
Rest the dough. Pat each piece into a ball. Flatten slightly, wrap in plastic and refrigerate for at least 30 minutes or overnight. (You can freeze 1 ball for later, or roll out both and freeze the cut pasta.)
Roll out the dough. Place the dough on a lightly floured surface and dust with flour. Starting in the middle, push away from you with a rolling pin, easing up on the pressure as you approach the edge. Continue rolling the dough into a sheet, turning occasionally, until you can see your fingers through the bottom. Let dry about 10 minutes.
Cut the pappardelle. Dust the top of the sheet of dough with flour and loosely roll it into a cylinder. Using a sharp knife, cut into 3/4-inch-wide slices. Unwrap the noodles; dust with semolina and gently toss to separate. Place on a sheet pan and cover with a tea towel until ready to cook (or freeze in freezer bags for up to 2 months).
Photograph by James Baigrie
Recipe courtesy Michael Chiarello for Food Network Magazine