In a bowl, whisk together the water, salt and egg.
In a stand mixer fitted with the dough hook or in a bowl with a wooden spoon, combine the flour with the water mixture until a smooth dough forms, about 2 to 3 minutes. Remove the dough from the bowl and form into a ball. Cover with plastic wrap and refrigerate for 1 hour.
Cut the dough into 3 or 4 equal pieces. Using a pasta roller or rolling pin, roll one piece of dough at a time into a thin strip 1/8 inch (3 mm) thick.
Cut each strip of dough into 2 ½-inch (6 cm) squares. Use to make your own dumplings. The wonton wrappers will keep in the freezer in an airtight container, separated by parchment paper.