Preheat the oven to 425°F - 220°C.
In a pot, put the water, salt and butter. Bring to a boil on medium heat.
In the meantime, weigh the flour and the eggs.Prepare the egg wash - beat the egg with a fork with a pinch of salt ; a glass of water with a fork ; a baking sheet lined with parchment paper and a piping bag with a round tip.
When the water starts to boil and the butter is dissolved, pour in the flour and mix straight away with a wooden spoon to dry the pastry, count 1 minute.
Once dried, place in the bowl of your stand mixer and mix for a couple minutes with the paddle on medium speed so that the steam goes away and the choux pastry finish drying out.
Keep mixing, adding one egg at a time and scraping the bowl each time.
Place the dough in the piping bag and stick the parchment paper with a bit of dough in the corners.Pipe Ø 1.2 inch - 3 cm choux, leaving some space between them.
Egg wash lightly with a brush and flatten softly with the fork - dip it in the water every other choux so it doesn't stick.
Sprinkle pearl sugar.
Put in the preheated oven and turn it off for 10 minutes.
Turn the oven back on at 330°F - 165°C, and keep baking for 20 more minutes. Don't open the door!
Allow to cool down at room temperature.