Pre-heat the oven to 350°F (180C/165C Fan) and line a baking tray with parchment or a silicone baking mat. For consistency in your finished product, you can pre-draw guiding lines onto the underside of the parchment for your eclairs - mine were about 3.5" (8cm) long, spaced 1.5" (3cm) apart.
Begin by placing the butter, salt and sugar in a medium saucepan. Add the water to the pan and bring to a boil over medium-high heat. Once boiling, tip in your flours and quickly beat with a wooden spoon until a dough forms. Continue mixing over the heat for a couple of minutes to help cook the flour out, then tip the mixture into a medium bowl and continue beating until it finishes steaming.
Once the dough has stopped steaming, you should add your eggs one at a time, mixing with the wooden spoon until incorporated after each addition. You may not need all three eggs, but you are looking for a smooth, dropping consistency of batter. Once this has been reached, put your batter into a piping bag, fitted with a nozzle about .5" (1.5cm) wide.
Pipe out steadily in lines on your parchment paper. Brush with some beaten egg to help develop a golden colour and place in the oven to bake. Once risen and lightly golden (about 30 minutes), turn off the oven and leave inside for another 30 minutes to help dry out. Then remove and leave to cool on a baking rack.