How to Make It
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.
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.
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.
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.
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.
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. Transfer the capellini to shallow bowls. Top with grated Parmigiano and garnish with shaved black truffle, if desired, and snipped chives. Serve right away.
Doppio zero (“double zero,” or 00) is a fine Italian flour available at specialty food shops and amazon.com.