In a bowl, mix sourdough discard, egg, olive oil, and salt until combined.
Gradually add flour and mix until a shaggy dough forms.
Knead on a floured surface for 6 to 8 minutes until smooth and elastic.
Cover and let the dough rest for 20 to 30 minutes.
Divide dough and roll into thin sheets about 1 to 2 mm thick.
Dust with flour or cornstarch, roll loosely, and slice into noodle strips.
Unroll noodles and toss lightly with flour to prevent sticking.
Bring salted water to a boil and cook noodles for 2 to 4 minutes.
Drain and serve immediately with desired sauce or broth.