Preheat the oven to 425°F. Line a baking sheet with parchment paper or a silicone baking mat.
In a medium saucepan over medium heat, combine 1 cup water, 1 stick (1/2 cup) butter, and 1 good pinch of salt. Bring to a simmer, with the butter fully melted.
Remove the pan briefly from the heat and add 1 cup all-purpose flour all at once. Return to medium-low heat and stir vigorously and continuously with a wooden spoon or spatula in one direction until the mixture forms a smooth dough that pulls away from the sides of the pan. Continue stirring and cooking for 1–2 more minutes to dry the dough slightly.
Remove the pan from the heat. Either transfer the dough to the bowl of a stand mixer fitted with the paddle attachment or leave it in the pan. Let the dough cool for about 4–5 minutes before adding eggs so they do not cook when incorporated.
Add 4 large eggs to the dough one at a time, mixing quickly and thoroughly after each addition (use the stand mixer, a hand mixer, or vigorous stirring by hand). Wait until each egg is fully incorporated and the dough is smooth and glossy before adding the next egg. The dough will change from shiny to slippery to a thicker, pipeable consistency.
Prepare a piping bag (or a large resealable plastic bag) by filling it with the dough. Snip off about 1/4 inch of the tip. Pipe mounds of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Wet your fingertip and gently press down any sharp peaks on the tops of the piped puffs so the peaks do not burn while baking.
Bake at 425°F for 10 minutes. Without opening the oven door, reduce the oven temperature to 350°F and continue baking for an additional 18–30 minutes, depending on puff size, until the puffs are puffed, dry, and golden brown.
Remove the puffs from the oven and transfer to a wire rack to cool. Allow them to cool before filling or serving.