Into the bowl of a stand mixer fitted with a dough hook, add All-Purpose Flour (2 cup), Salt (3/4 teaspoon), Water (1/3 cup), and Egg (2). Mix on low speed for 2-3 minutes, until dough comes together.
Knead on low speed for another 3-4 minutes.
Wrap the dough in plastic wrap. Let rest for 30-45 minutes.
Divide dough into 4 equal parts. Re-wrap any dough you aren't currently using. Fold dough into a square.
Using a pasta machine on the widest opening, crank your dough through. Fold each side into the middle, then run it through again.
Switch pasta machine to the next narrowest setting and run it through twice. Repeat, switching to increasingly narrow settings, until you reach the smallest setting. When dough gets too long, cut it in half and continue.
Trim dough into squares.
Refrigerate egg roll wrappers for later, or use right away. If stacking, dust each side with flour so they don't stick to each other.