Melt butter and heat water and milk. In a medium saucepan, add the water, milk, butter, sugar and salt, and heat on low until the butter is melted and the sugar has dissolved. Increase the heat to medium to high and bring to a rolling boil.
Add flour. Remove the pan from the heat and add the flour immediately. With a wooden spoon, mix together vigorously until completely combined.Then return to medium-high heat and beat for 2 minutes until the mixture comes away from the sides of the pan and forms a ball. You’ll see a film form on the base of your saucepan, and you’ll know it’s ready. (Use a digital thermometer for accuracy- the panade should be between 75°C to 80°C (165°F and 175°F)
Beat to release steam. Remove the pan from the heat and place it in the bowl of a stand mixer fitted with the paddle attachment. Beat for 1 minute on low speed to release some steam. Use a digital thermometer for accuracy- the panade should get to 60°C (140°F) or under before continuing on with the next step. In a small jug, whisk the four eggs together.
Please read this step before continuing as the amount of egg added can vary. With the mixer running on low speed, slowly pour in ¾ of the whisked eggs in 3 to 4 separate additions, mixing for 30 seconds between each addition. Scrape the sides and base of the bowl halfway through. It may look curdled and slimy to start with but will come together as you beat the mixture. Once the eggs have been fully incorporated, beat the mixture for a further 2 minutes. Note on the perfect consistency. The choux pastry should be smooth and shiny and should hold its shape when a finger is passed through the mixture. When the beater is pulled up out of the batter, a thick V-shaped ribbon forms, of smooth dropping consistency. If your pastry has not achieved this consistency, add the remaining egg a teaspoon at a time and test the consistency again. If you need more egg, then whisk the 5th egg in a small bowl, and add a tiny bit at a time. Set aside any remaining egg to be used as egg wash.
Chill the dough. Preheat the oven to 200°C (390°F). Fill a piping bag fitted with a round piping tip, close the open end of the piping bag and refrigerate for 30 minutes Preheat the oven to 200°C (390°F). Pipe choux onto the baking tray. Line a large baking tray with parchment paper. Whilst holding the piping bag upright and keeping the tip of the piping tip touching the choux pastry, pipe 4cm (1.5-inch) wide mounds onto the prepared tray. Keep them 2.5cm (1 inch) apart. Prep choux on the tray. Using a pastry brush dipped in water, brush the parchment paper around the mounds. Using the tip of your finger dipped in water, smooth the points of each mound. Add milk to the remaining egg and whisk together. Brush this egg wash gently over the top of the choux pastry mounds.
Bake. Place the tray in the oven and immediately reduce it to 180°C (350°F) and bake for 25 to 30 minutes, or until golden brown and crisp. Don't the oven door in these first 25 minutes of baking. Remove the buns from the oven and skewer a hole in the bottom of each choux bun to allow the steam to escape. Return to the oven for 5 to 10 minutes, and then allow to cool completely on the baking tray.