In a medium saucepan, combine the water, salt, sugar, and butter. Bring the mixture to a boil over medium heat, stirring occasionally until the butter melts completely.
Once the mixture is boiling, remove it from heat and add the flour all at once. Stir vigorously with a wooden spoon until the dough pulls away from the sides of the pan and forms a ball.
Allow the dough to cool for about 5 minutes. Then, add the eggs one at a time, mixing well after each addition. The dough should be smooth and glossy. If you like, you can incorporate a splash of vanilla extract for added flavor.
Preheat your oven to 400°F (200°C). Transfer the dough to a piping bag fitted with a large round tip. Pipe small mounds (about the size of a golf ball) onto the prepared baking sheets, leaving space between each one.
In a small bowl, whisk together the egg yolk and milk. Brush the tops of the piped mounds with the egg wash and sprinkle generously with pearl sugar.
Place the baking sheets in the preheated oven and bake for about 20-25 minutes, or until the chouquettes are puffed and golden brown. Avoid opening the oven door during baking, as this can cause them to deflate.
Once baked, remove the chouquettes from the oven and let them cool on a wire rack. Enjoy them warm or at room temperature!
