Preheat the oil at 320F degrees while you make the churro batter. You can use a candy thermometer to check the temperature.
Place the water, vanilla extract, salt, and butter in a saucepan at medium- high heat.
Once it comes to a rolling boil, stir in the flour all at once. It is very important that the water is boiling to ensure that the dough will render crispy churros.
Mix the dough vigorously using a wooden spoon or spatula. You have to do this step very quickly.
Remove the saucepan from the heat, wait about a minute, then add the egg. Keep mixing until the egg is completely integrated into the dough (you can use a mixer for this step). In the beginning, the dough will want to separate after adding the egg, but keep mixing until the ingredients are well combined and you have a smooth and soft dough that separates from the bottom of the pot. This step will take a few minutes.
Place the dough in the pastry bag fitted with a star-shaped tip. Make sure there aren’t any bubbles of air in the dough while you place it inside the bag.
Pipe 6-inch strips of dough on a prepared tray and then fry them (see notes). You can also pipe the strips of dough directly into the hot oil, cutting them with your kitchen scissors. The oil will start bubbling when you add the raw churro, and at this point you must not touch the oil or the churro, to avoid having an explosion.
Fry the churros for about 2 to 2.5 minutes in hot oil ( 320F) until golden brown (in total it should take 4-5 minutes to cook each churro), and then turn the churros to have an even crispiness and golden color.
Once they are golden, remove from the heat, place on the paper towel to drain for a few seconds, and then roll in the sugar.