Preheat the oven to 425F. Line a large sheet pan with parchment paper.
In a large saucepan, bring the water, butter, sugar, and salt to a boil over medium-high heat. When it boils, immediately take the pan off the heat.
Add all of the flour at once and stir hard with a wooden spoon until all of the flour is incorporated. Return to medium heat and cook, stirring for about 60 seconds.
Scrape the mixture into the bowl of a stand mixer fitted with a paddle attachment (you can also use a hand mixer). Beat at medium speed for about 2 minutes to cool the mixture down. (it will still be warm.)
With the mixer running, add 3 eggs, one at a time, stopping to scrape down the sides of the bowl between each egg. Mix until the dough is smooth and glossy and the eggs are completely incorporated. The dough should be thick but fall slowly and steadily from the beater when lifted out of the bowl. If the dough is still clinging to the beater, add the remaining 1 egg and mix until incorporated.
Transfer the dough to a pastry bag fitted with a large round tip and pipe dollops roughly 2 inches in diameter and 1 inch high. Lightly wet a finger and tap down the spike on top. (For additional color during baking, you can brush the tops of the dough lightly with an egg wash.)
Bake for about 20 minutes or until the dough is golden brown and appears dry. (Try not to open the oven door during the bake.) Remove the baking sheet from the oven. Carefully poke holes in the side of each puff by inserting the tip of a small knife about halfway into the puff. Return to the oven and bake for another 3 minutes. Remove and let cool completely on the baking sheet. (You can turn the oven off and leave the puffs in the oven with the door cracked open after baking if you'd like them to really dry out.)