In a large bowl, mix the flour, 60 ml ice-cold water, egg, and salt until a sticky dough forms. Add up to 60 ml more ice water if needed to achieve the correct consistency.
Turn the dough out onto a lightly floured surface and knead for about 5 minutes, until smooth and elastic.
Let the dough rest for 30 minutes, then knead it briefly again.
Divide the dough ball in half, wrapping one half in plastic wrap to keep it from drying out.
Roll the other half of the dough on a lightly floured surface until it is about 3 mm (⅛ inch) thick or thinner.
Cut the dough into squares measuring about 9 cm (3 ½ inches) on each side.
Dust each square lightly with cornstarch and stack them to prevent sticking.
Repeat the rolling and cutting process with the remaining dough. Use the wrappers immediately or freeze them for later use.