Mix together the flour and salt with clean fingers on your work surface.
Create a well in the center of the flour and add the egg, whisking slowly to incorporate the flour.
Add the water a little at a time and work the dough until it holds together and forms a ball.
Using your hands, knead the dough for 5-6 minutes to develop the gluten.
Cover the dough and let it rest for 30 minutes.
After 30 minutes, knead the dough again for 2 minutes.
If you have a pasta roller, pass the dough through the pasta machine on its thinnest setting. (If you don't have a pasta machine, roll the dough into a long rope and cut the rope into 40-50 small pieces. Use a dough roller to roll each piece into 4-inch circles.)
After thinning the dough through the pasta roller, cut the dough sheets into 4-inch circles, or about the size of the wide mouth of a mason jar. (You could also cut them into rectangles.)
To keep the wonton wrappers from sticking together, dust them each with flour and stack them in a pile, wrapping the pile in plastic wrap. Freeze until ready to use.
To thaw the wrappers, take them out of the freezer and place them in the refrigerator for 2-3 hours.