Place the flour, semolina and salt in the bowl of a food processor and pulse several times to combine the ingredients.
Add the egg all at once and process for 30 seconds, drizzling the oil through the opening in the lid. The dough should look like coarse, wet sand.
Dust a work surface generously with semolina.
Transfer the dough to the work surface and bring it together in a ball.
Knead the dough for a good 3 or 4 minutes, using the heels of your hands to push it away from you again and again, and occasionally rotating the dough 180 degrees. The dough should appear smooth and silky when you are done; it should not be sticky.
Wrap the dough in plastic wrap and let it rest for 20 minutes.
Set up the pasta maker next to a work surface.
Sprinkle a rimmed baking sheet liberally with semolina.
Sprinkle the work surface with semolina. You'll need to keep it dusted with semolina at all times so the pasta doesn't stick as you roll and cut it.
When ready to roll out the pasta, cut it into quarters. Work with one quarter at a time and keep the remaining portions wrapped.
Use your fingers to work the dough into a rough 3-by-4-inch rectangle. (The dough should have the texture of Play-Doh.).
Use the heel of your hand to flatten the dough to a thickness of 1/2 inch.
Pass the dough through the highest (thickest) setting of your pasta machine.
Fold it into thirds, as you would a business letter, then flatten it to 1/2 inch and pass it through the machine again. Fold, press and roll one more time.
Set the rollers on the next-highest setting and pass the dough through twice. (You don't have to fold it.).
Continue to lower the setting one increment at a time, passing the dough through twice each time, until your dough reaches the desired thickness.
Setting 3 is good for fettuccine and lasagna sheets.
Setting 2 is good for filled pastas, such as tortellini, ravioli and agnolotti, or for thinner lasagna sheets.
Use plenty of semolina to keep the dough from sticking to itself as it falls into accordion folds while coming out of the rollers.
If you're making filled pastas, make them as you go, one sheet at a time. (If you roll all the sheets beforehand, they will dry out and might tear as you try to work with them.).
If you’re not making filled pasta, use a knife to slice the sheets into lasagna noodles or use your machine’s cutters to make fettuccine or spaghetti.
Use plenty of semolina as you stack lasagna noodles (alternate the layers lengthwise and crosswise) or form piles of cut pasta, fluffing them with semolina so they remain separate.
Transfer the finished pasta to the prepared baking sheet as you work.
TO FREEZE: When you have finished rolling and cutting all the pasta, transfer the baking sheet to the freezer for an hour or two, until the pasta is frozen. Wrap it in plastic or store in resealable food storage bags and freeze for up to a month. (It is a good idea to weigh the pasta and freeze it in portions.).
MAKE AHEAD: The dough can be made a few days in advance, wrapped tightly in plastic wrap and frozen. The uncooked pasta can be frozen in portions for up to 1 month.
NOTE: Depending on the humidity, the size of your eggs and the brand of flour you are using, you might have to adjust the amount of oil you add to achieve the desired texture. Weighing the flour and the eggs rather than relying on our uneven American measuring methods leads to more consistent results.
NOTE: To make saffron fettuccine, combine the oil with a half-teaspoon of saffron threads in a small bowl and microwave on HIGH for 30 seconds. Allow the oil to cool, then add it and the threads to the dough.