Preheat the oven to 200°C (400°F). Line 2–3 baking trays with parchment paper.
Sift the flour into a bowl.
Place the butter, water, sugar, and salt in a medium-sized saucepan. Bring to a boil over high heat. As soon as the mixture comes to a boil (the butter will already have melted), remove the saucepan from the heat and add the flour.
Stir quickly with a wooden spoon until the mixture forms a ball and pulls away from the sides of the saucepan. Return the saucepan to low heat and continue stirring the mixture for another 2 minutes.
Turn off the heat and transfer the entire mixture to the bowl of a food processor or stand mixer. Process for 1 minute, then gradually add the eggs while the machine is running. Process or beat on high speed until the mixture is smooth, glossy, and homogeneous.
To shape the choux, you can use two teaspoons: use one to scoop up some of the dough and the other to push it onto the parchment paper. Alternatively, you can use a piping bag fitted with a round 1 cm (½-inch) nozzle. Do whatever works best for you.
Shape small choux, approximately 3 cm in diameter, and arrange them in rows on the baking trays.
Bake in the preheated oven for 15 minutes. Reduce the temperature to 175°C (350°F) and bake for another 15 minutes.
Remove the choux from the oven and, using a small knife or skewer, make a small hole in the side of each one to allow the steam to escape.
Return the choux to the turned-off oven with the door slightly ajar. You can place a wooden spoon in the door to keep it from closing completely. Leave them in the oven for 1 hour.
The choux should be crisp, not soft. Allow them to cool completely. At this stage, you can store them in a large airtight container or plastic bag in the refrigerator for up to a week.
If they become soft, you can place them back in a moderately low oven for a short while to crisp them up again.