In a bowl, combine eggs, water, and sesame oil, if using, and whisk until frothy. Add in flour and salt, then mix until a shaggy dough forms.
Knead the homemade egg noodle dough with lightly floured hands for 8-10 minutes until completely smooth. It should feel soft but not sticky, and elastic, rather than crumbly. Cover the dough in plastic wrap and let it rest for 30 minutes. This relaxes the gluten and makes rolling easier.
Cut the dough into quarters, then roll each piece into a ball and cover to keep from drying. Use a rolling pin to roll out the dough on a floured surface until it reaches the desired thickness.
Gently fold the dough into 4 layers, sprinkling a little flour between each fold, then cut into strips using a sharp knife or pizza cutter. Unfold each strip, cutting if desired. Repeat until all 4 dough balls have been cut into your preferred noodle shape.
Notes
I recommend starting with 3 eggs, then adding an additional egg if needed, as eggs can vary in size.
If dough is sticky, add more flour. If the dough is too dry, sprinkle in some water, ½ teaspoon at a time.
Cover the dough balls and the noodles as you cut them to keep them from drying out.
Let the dough rest for a minimum of 30 minutes, or up to 2 hours. This will make it much easier to roll.
Dust noodles generously with flour to keep them from sticking to each other.
Be careful not to overcook! Fresh egg noodles cook much faster than dry ones.
Because these noodles contain eggs, improper storage can lead to spoilage. Only store fully dried noodles at room temperature. Fresh noodles can be stored in the fridge for 2-3 days or in the freezer for up to 3 months.