Step 1: Sift both flours with the caraway and 1 1/2 tablespoons of salt into a large bowl. Make a well in the center and add the egg yolks, whole egg, olive oil and 1 tablespoon of water. Using a fork, gradually whisk the flour mixture into the wet ingredients until a shaggy dough forms. Scrape the dough out onto a work surface and knead until very stiff but smooth, about 15 minutes. Wrap in plastic and let rest at room temperature until softened and relaxed, about 2 hours.
Step 2: Divide the dough into 12 pieces and work with 1 piece at a time; keep the rest covered. Press the dough to flatten. Set up a pasta machine to roll flat pasta. Starting at the widest setting, run the dough through successively narrower settings until it’s a scant 1/8 inch thick. Transfer the sheet to a lightly floured work surface and dust with 00 flour. Repeat with the remaining pieces of dough.
Step 3: Set up a pasta machine with a capellini cutter. Working with 1 sheet of dough at a time, gradually feed the dough through the cutter. Gently toss with 00 flour and transfer the capellini pile to a lightly floured baking sheet. Repeat with the remaining sheets of pasta to form 12 piles.
Step 4: In a small saucepan, whisk the cream with 2 tablespoons of water and the yeast and cook over moderately low heat, stirring, until the yeast is dissolved and the mixture is very thick, 3 to 5 minutes. Whisk in the unsalted butter 1 tablespoon at a time until emulsified, then season with salt and pepper.
Step 5: In a large saucepan of salted boiling water, cook the pasta until al dente, about 1 minute. Drain, reserving 1 cup of the cooking water. Wipe out the saucepan.
Step 6: In the large saucepan, melt the yeast butter with the truffle butter and orange zest over moderately high heat. Add the pasta, the 1/4 cup of Parmigiano and 1/2 cup of the reserved cooking water and toss until hot and evenly coated with the butter, about 2 minutes. Add a little more of the cooking water if necessary.