Preheat the oven to 400°F. Place the water, butter, and salt in a small saucepan and place over medium-high heat. Bring the water to a rolling boil and melt the butter.
Reduce the heat to low and add all of the flour in one go. Using a wooden spoon, integrate the flour into the water mixture, working out any lumps, until a thick paste forms. Continue to cook the paste until a film forms on the bottom of the saucepan or the paste registers 175°F on a probe thermometer.
Transfer the dough to a stand mixer fitted with a paddle attachment. Beat the dough until it cools to 145°F. Beat the eggs into the dough one at a time. Beat the last egg into a ramekin and add only enough to form a thick glossy dough that falls like a ribbon from the paddle.
Transfer the dough to a pastry bag fitted with a small round pastry tip ( I used a #12). Line a large baking sheet with parchment paper. Squeeze a dollop of the choux pastry on all four corners to anchor the parchment paper. Pipe 1 inch rounds of the pastry well-spaced apart. You should have 20.
Wet your index finger with a little water and tap each round to flatten the peak. Gently brush with a little egg yolk and transfer to the oven. Bake the choux for 20-25 minutes or until golden.
Take the puffs out of the oven and let cool slightly. While still fairly hot, cut small holes in the bottom of each puff. You can refine the shape when they cool completely. This is more or less to release steam. Set the puffs aside to cool completely.