In a medium bowl, whisk together egg, cold water and salt. Mix in all-purpose flour 1/3 at a time. Allow the mixture to stand 15 minutes at room temperature.
Heat a wok over high heat. Remove from heat and thinly coat with 1 tablespoon peanut oil. Reduce heat to low. While wok is still warm, pour 1/4 of the egg mixture in an approximately 8 inch circle. Rotate wok quickly to spread an even layer of batter. Cook over low heat 45 seconds to 1 minute, until bottom is golden brown and edges begin to curl. Carefully remove from heat and place on a paper towel, golden brown side down.
Repeat the wok procedure with remaining batter, 1/4 at a time. Rub wok with remaining tablespoon of peanut oil after the second wrapper has been made.
Allow the wrappers to cool completely. Cut wrappers in half to use for egg rolls.