Mix water, sugar, salt, butter, and vanilla together in a pot.
Place the pot on a hot stove and heat until the butter is melted and it starts to boil gently.
Add the flour and whisk the mixture until it's as smooth as possible.
Add one egg at a time, whisking until the dough is soft and smooth.
Place the dough in the refrigerator for about 25 minutes to firm up a bit.
Prepare the frying oil (heat it to around 180 degrees Celsius (356 degrees Fahrenheit) - if using a pot, you can check if it's hot enough by dipping the wooden end of a matchstick or a piece of bread into the oil - it should sizzle around it if it's hot enough).
Put the dough into a piping bag fitted with a star nozzle.
Fry your churros in the oil for a few minutes until golden brown.
Turn them occasionally during frying.
Place the finished churros on paper towels to absorb excess oil.
Sprinkle with powdered sugar and serve immediately.