In a medium mixing bowl, whisk the water and egg until smooth. In a stand mixer bowl, combine the flour, baking powder, and salt. Add the cold butter and then pour in the egg-water mixture. Mix using a dough hook until no dry flour remains.

Lightly knead the dough on a floured surface for about 30 seconds until smooth. Shape the dough into a log about 3/4-inch thick, cover it, and refrigerate for at least 1 hour.

Remove the dough and let it come to room temperature for 30 minutes. Roll it into a 10-inch by 6-inch rectangle. Cut the dough into ten long strips. For a paired texture, lay two strips on top of each other and lightly moisten one side with water, then press down along the center using a chopstick.

Heat vegetable oil in a deep fryer or deep pan to 400°F. Gently lower one paired dough strip into the oil. Immediately use chopsticks or tongs to turn and stretch the dough continuously so it puffs up evenly. Fry until the youtiao turns light golden, about 90 seconds. Remove and drain on paper towels. Optionally, sprinkle a pinch of salt.

Serve the youtiao warm. They are best enjoyed fresh.