On a work surface, mix together the flour, baking soda, and salt. Make a well in the center and add the eggs to the well. Using the fingers of one hand, work the eggs into the flour mixture until all of the eggs are absorbed. Slowly dribble in the water, mixing with your fingers as you pour, until the water is thoroughly absorbed and the ingredients begin to adhere to one another. Using a dough scraper, pick up the mixture from the work surface and then knead it on the work surface for about 10 minutes, or until it becomes an elastic dough. Cover the dough with a damp cloth and allow to rest for 3 hours.
When the dough is ready, lightly dust the work surface with a little of the cornstarch. With a rolling pin, roll out the dough into a sheet ¼ inch thick. Pick up the sheet, dust the work surface again with cornstarch, and continue rolling the dough until it is ⅛ inch thick. Roll the dough around a wooden dowel about 1 inch in diameter or a length of broom handle. Dust the work surface again with cornstarch and unroll the dough sheet onto it. Roll the dough again with the rolling pin until it is about 1/16 inch thick, then roll it around the dowel again. (The only way you can pick up the dough is by rolling it around the dowel; otherwise, it will tear.) The dough should be quite thin at this point.
Dust the work surface again with cornstarch and unroll the dough sheet on it. Roll the sheet with the rolling pin until it is about 22 by 20 inches. It should be thin enough that, if you lift a corner, you will be able to see light through it. Roll the dough sheet around the dowel again and then dust the work surface again. Then, using the edge of the dough scraper and a ruler, cut out 3-inch squares. Stack the squares, dusting between the layers with cornstarch. To ensure the squares remain pliable, wrap them well in plastic wrap, then refrigerate them overnight. Even though you use rounds for making the dumplings, it is best to cut squares now because you will get a better yield from the sheet. You will also have more control when you trim squares into rounds than if you cut rounds from the sheet.
These homemade skins are now ready for use. You should have about 40 wrappers. Each of the dumpling recipes makes 36 dumplings, so you will have a few extra wrappers as insurance against mistakes when forming the dumplings. As you fill the wrappers, work with 1 wrapper at a time and keep the others covered with a damp cloth to prevent them from drying out. If you decide to use commercial wrappers, treat them the same way.