Make the Dough: In a large bowl, combine the flour and salt. Make a well in the center and add the eggs, sourdough starter (or discard), and olive oil. Mix with a fork until the dough starts to come together, then knead by hand until smooth and elastic, about 5 to 8 minutes. If the dough is sticky, add a bit more flour; if dry, add a few drops of water.
Rest the Dough: Form the dough into a ball, cover it, and let it rest for at least 30 minutes at room temperature.
Roll the Dough: Divide the dough into smaller portions. Roll each piece thin using a rolling pin or pasta machine. Lightly dust with flour to prevent sticking.
Cut the Pasta: Cut the dough into your preferred shape (fettuccine, angel hair, tagliatelle, etc.).
Cook the Pasta: Bring a large pot of salted water to a gentle boil. Cook fresh pasta 2 to 4 minutes until tender. Drain and serve immediately.