In a large glass mixing bowl or in the bowl of a stand mixer, combine the flour and salt. Add whisked egg and olive oil to the flour. Mix to combine.
Knead the pasta by hand or using the dough hook of a stand mixer until it turns elastic and is no longer sticky.
Cut dough into three pieces and roll each into a ball. Wrap each ball tightly with a plastic wrap and refrigerate for about 20 minutes.
On a floured surface, roll out the dough pieces into thin layers (you should be able to almost see through it). Let the dough hang on a pasta dryer or sit flat on a floured surface to dry for about 15-20 minutes. If you are going the floured surface route, flip the pasta over every 5 minutes. The dough should be dry, but not so dry that it breaks apart easily.
Using a sharp knife/pizza cutter, pasta cutter, or stand mixer pasta attachment (see instructions for each above), slice the pasta dough to your preference (fettuccine, lasagna, angel hair, etc). Cook immediately or refrigerate or freeze for later use.