Place butter and water in a saucepan and heat until butter melts. (Do not allow water to simmer.) Once butter has melted, increase the heat and bring to a rapid boil. Take the pan away from the heat and add the flour. Use a wooden spoon to stir in quickly to form a smooth paste.
Return pan to the heat until dough looks dry and forms a ball. It should pull away from the sides of the pan.
Slowly add the eggs (put off the heat again so that the eggs do not cook), beating well after each addition. Continue to beat until the paste is thick and shiny.
Pipe the choux pastry directly onto a lightly greased baking sheet (apply a little pressure when piping, to keep the shapes as uniform as possible).
Lightly brush the choux fingers with egg wash and score with a fork dipped in the egg wash.
Bake at 220°C for 15-20 minutes or until puffy, golden brown and risen. Transfer éclairs onto a wire rack to cool completely.
When ready to fill, pierce each éclair at both ends with the tip of a small knife, then pipe filling into the opening.