Combine water and butter in a medium saucepan and bring to the boil over high heat. Cook, stirring, for 3-4 minutes or until butter melts. Remove from heat.
Add the flour and salt and stir with a wooden spoon until well combined and the dough comes away from the side of the saucepan. Cover with plastic wrap and set aside for 15 minutes or until cool.
Add the eggs, 1 at a time, beating well after each addition, until well combined. Spoon dough into a piping bag fitted with a 2cm-diameter fluted nozzle.
Add enough oil to a large saucepan to reach a depth of 6cm. Heat to 180°C over medium heat (when oil is ready a cube of bread will turn golden brown in 15 seconds). Using a small sharp knife to cut the dough, pipe four 10cm lengths into the oil. Deep-fry for 1-2 minutes or until golden brown. Use a slotted spoon to transfer churros to a plate lined with paper towel. Dust with icing sugar. Repeat with the remaining dough, reheating oil between batches.
Meanwhile, combine the chocolate and milk in a medium saucepan over medium heat. Cook, stirring, for 5 minutes or until chocolate melts and the mixture is smooth.
Arrange churros on a platter and serve with chocolate dipping sauce.