Combine the water, salt, butter, and sugar in a saucepan and bring to a simmer over high heat. There's no need to stir.
Remove pan from the heat add the flour all at once. Stir in the flour then return to the stovetop over medium heat. Stir with a wooden spoon for about 3 minutes, or until the mixture forms a cohesive mass and pulls away from the sides of the pans, leaving a film of flour on the sides of pan.
Transfer the mixture to a bowl or a stand mixer and beat it with a wooden spoon or the paddle attachment for about 1 minute or until slightly cooled. This may take a few extra minutes (internal temperature should be about 121oF)
Beat in the eggs, 1 at a time, until you've added 4. Check the consistency of the batter by pulling a wooden spoon through it. When the groove it makes slowly in on itself, you've added enough eggs. Another way to check is to see if the batter droops from the spoon when it is held sideways. If so it is ready. While the dough is best used right away, it will keep for several hours in the refrigerator.
Preheat the oven to 400F. If making cream puffs: Fit a pastry bag with a 1/2-inch plain tip and fill it with the dough. Prepare a cookie sheet with parchment paper or silicone baking mat. If using paper, pipe a small amount of dough underneath the paper in the four corners to hold it down. For eclairs I like to use a French star tip.
For cream puffs (and profiteroles): Make 2 rows of 3 each cream puffs each. Start by holding the pastry bag about 3/4-inch above the sheet pan and squeezing. If the pastry bag tip is too close, the cream puffs won't be thick enough; if it's too far away, they won't be wide enough. As the round of pastry takes shape, lift the pastry bag until it is about 1 1/2 inches above the sheet pan. The mounds of dough should be about 3 1/2 inches in diameter and about 1 1/2 inches high in the center. Brush with an egg wash, lightly smoothing the surface with the brush at the same time. Bake the cream puffs for about 20 minutes or until puffed and golden. Turn down the oven to 300F and continue baking for 20 minutes more. Let cool for at least 20 minutes on a cake rack.