In a large stainless steel bowl, stir together the flours and kosher salt.
Create a well in the center and add the large eggs and olive oil. Gradually mix the egg mixture into the flour using a fork or your fingers, eventually bringing the ingredients together to form a firm dough. (You may need to add a few drops of water if the dough feels too dry.)
Transfer the dough to a flat surface and knead the dough until it's smooth, 3-5 minutes. (Try to refrain from adding extra flour when kneading as this will give your pasta a floury taste.)
Dribble a little olive oil over the dough and place in a plastic bag. Allow to rest for 30-40 minutes.
Roll and Cut the Pasta
Divide the pasta in half, returning the extra dough to the bag until ready to use. Flatten one piece of dough with a rolling pin to match the size of your pasta roller.
Feed the dough through the machine, using the first setting of your machine (I use a KitchenAid Pasta Roller and mine is 2). Pass the pasta through once, and then fold it into thirds and pass it through again.
After that, continue feeding the pasta sheet through the machine at each level (3, 4, 5...) until you reach the desired thickness.
Once you have the pasta dough to the desired thickness, feed the sheet through the cutter attachment, catching the pasta as it comes out the other side.
Drape finished pasta on a drying rack or form into little nests on a floured surface to dry, if desired. Repeat with the other ball of dough.
At this point, the pasta is ready to cook, or you may continue allowing it to dry. I like to dry my pasta for 2-3 hours, but it's not necessary. If you plan to freeze or store the pasta in your pantry, allow it to dry for 24-48 hours before placing in a storage container or Zip-lock bag.
Cook the Pasta
Cook the pasta in boiling salted water until al dente or firm to the bite 2-4 minutes, depending on the thickness of your pasta. (Fresh homemade pasta doesn't require as much cooking time as store bought pasta.)
Stir the pasta immediately after you add it to the water and then once more while it cooks to prevent it from sticking.
Serve immediately with your favorite sauce--even just a drizzle of olive oil or melted butter. This recipe makes 4-6 servings.
Notes
*Sometimes if I desire a softer dough, I will use 1 1/2 cups 00 flour and 1/2 cup Semolina, with everything else the same. I will do this when making Ravioli, Lasagna noodles, and also Pappardelle.