Preheat the oven to 200°C (conventional oven). Line 2 baking trays with greaseproof paper and set aside.
Place the butter, water, milk and salt into a saucepan over medium heat. Allow the butter to melt, then bring to a strong simmer.
Remove the pan from the heat and add the sifted flour, all at once. Mix the flour in off the heat, then return the pan to the heat.
Stir the mixture over the heat for a couple of minutes, taking care not to scrape the bottom of the pan as you stir, until the mixture reaches 75°C.
Transfer the dough to a bowl and stir for a few minutes until the mixture has cooled slightly (it should be about 60°C).
Gradually add the beaten egg, stirring well between each addition, until all of the egg has been incorporated and the mixture resembles a smooth paste.
Transfer the choux pastry to a piping bag, fitted with a small, open-star nozzle. Pipe lengths of about 4-5cm onto the prepared baking trays to make the éclairs.
Bake one tray of éclairs at a time in the preheated oven, for about 15 minutes, or until the éclairs have puffed up and are crisp and golden.
As soon as you remove the éclairs from the oven, use a sharp knife/skewer to pierce each one, to allow the steam to escape. Allow the éclairs to cool completely before filling and decorating.