In a medium saucepan, place the water, butter, and salt and cook over medium heat until the butter has melted and the water comes to a boil.
Reduce heat to low and add the flour.
Use a wooden spoon to vigorously stir until you have a smooth ball of dough, about 2-3 minutes.
Transfer the dough to a bowl of a stand mixer (or a large bowl) and use the paddle attachment to mix on low and cook the dough. About 5 minutes.
Increase speed to medium-high and the eggs, one at a time. The mixture will look like it is curdle but as you mix it will become smooth.
Transfer the dough into a large piping bag fitted with a large round tip.
Preheat the oven to 400F. Line a baking sheet with parchment paper and use 1-2-inch round cookie cutter to mark circles, leaving about 2 inches of space for them to puff.
Turn the parchment paper so the pencil will face the pan, and pipe the dough.
Bake over the low (but the lowest) oven rack for ten minutes, then reduce the temperature to 375F and bake for an additional 13 minutes.
Turn the oven off and leave the puffs on the oven door shut for 10 minutes.
Remove from the oven. The pastries are now ready to be served. If you choose to fill them, allow them to cool completely.