This is my go-to recipe for fresh pasta. It also freezes really well, so I'll make a double batch and then toss some in the freezer for later! Recipe Source: Mastering Pasta The Art and Practice of Handmade Pasta, Gnocchi, and Risotto by Marc Vetri with David Joachim
Make the pasta dough: In the bowl of a stand mixer fitted with a paddle attachment, or on a work surface, combine both flours and make a well in the center. On medium speed, or using your fingers, mix in the egg yolks, oil and water, adding them one ingredient at a time and mixing just until the dough comes together, 2 to 3 minutes. If the dough seems dry, add another tablespoon of water.
Turn the dough out onto a lightly floured work surface and using the palms of your hands, knead the dough until it feels silky and smooth, about 8 to 10 minutes.The dough is ready when it gently pulls back into place when it is slightly stretched.
Shape the dough into a ball and then flatten the ball into a disk. Cover the dough with plastic wrap and let it rest at room temperature for at least 30 minutes or chill in the fridge for up to 3 days.
To roll out the dough, cut it into 4 equal pieces. Let the pieces sit, covered, at room temperature for 10 minutes if chilled.
Shape each piece into an oval wide enough to fit the width of your pasta roller. Lightly flour your work surface and set the pasta roller to its widest setting. Lightly flour 1 piece of dough, pass it through the roller and then lightly dust the rolled dough with flour, brushing off the excess with your hands. Pass the dough through the widest setting again. Lower the setting by 1 notch and continue to pass the dough through until you've reached the desired thickness. For tagliatelle, roll the dough to about ⅛-inch thick.
Fit the pasta machine with the appropriate cutter and run the pasta sheets through the cutter.
Using floured hands, toss the pasta to keep from sticking. Cover the pasta and refrigerate it until ready to cook.
When ready, add the pasta to the boiling salted water and cook it two thirds of the way through, 10 to 20 seconds. The pasta will finish cooking in whatever sauce you are making.
Drain the pasta, reserving ½ cup of the pasta cooking liquid.