Mix the flour, salt and 1 tablespoon of the sugar in a bowl. Pour the water into a saucepan and bring to the boil. Take off the heat, add the flour mixture and beat well. Then return to the heat and stir until it forms a smooth ball that leaves the sides of the pan almost clean. Remove from the heat and leave to cool for 10 minutes.
Gradually beat the whole egg, egg yolk then the vanilla into the flour mixture until smooth. Spoon into a large nylon piping bag fitted with a 1 cm (½ inch) wide plain tube.
Pour the oil into a medium-sized saucepan to a depth of 2.5 cm (1 inch). Heat to 170°C (340°F) on a sugar thermometer or pipe a tiny amount of the mixture into the oil. If the oil bubbles instantly it is ready to use. Pipe coils, S-shapes and squiggly lines into the oil, in small batches, cutting the ends off with kitchen scissors. Cook the churros for 2–3 minutes until they float and are golden, turning over if needed to brown evenly.
Lift the churros out of the oil, drain well on kitchen paper then sprinkle with the remaining sugar mixed with the cinnamon. Continue piping and frying until all the mixture has been used. Serve warm or cold. They are best eaten on the day they are made.