Preheat the oven to 400℉ and line your baking sheets with parchment paper.
In a medium saucepan, melt the butter with the water, sugar, and salt. Once melted, bring the mixture to a boil.
Remove from the heat and add all of the flour. Stir until combined, then place the saucepan back on a low- medium heat.
Cook the dough for 1- 2 minutes to evaporate some of the water in the dough. Use a wooden spoon or spatula to stir and press the dough around. It's done when you see oil beading on the surface of your pan (non-stick) or a film forms on the side (stainless steel).
Place the dough into the bowl of your stand mixer. Press it evenly along the bottom and a bit up the sides so that it can cool down. Allow the dough to cool for 5- 7 minutes.
Add and egg and beat on low until combined. Repeat with the next two eggs as well. Crack the remaining two eggs into a cup and mix with a spoon. Add this egg mixture a bit at a time, combining between additions, until you reach the right consistency. The choux pastry dough should be smooth, glossy, and form a V off the end of your spatula when you lift it up. It's best to have dough that is took thick than too thin.
Fill a piping bag fitted with a wide round tip with the choux pastry dough. Pipe mounds two inches apart onto the prepared baking sheets. Dip your finger into water and pat down any peaks. Brush the tops with an egg wash.
Gently sprinkle some water over the baking sheets. This will create steam and help them puff up.
Bake for 20 minutes. Drop the temperature to 350℉ and bake for another 5- 10 minutes, or until the puffs are golden brown. Watch them closely!
Immediately take the puffs out and pierce the sides with a sharp knife, making a small X. Place them back on the sheets and back into the oven. Crack the oven door. Let them cool in the oven like this for 10 minutes before removing the baking sheets. This will help prevent them from collapsing.