Preheat the oven to 375°F (190°C). Tear off a large piece of parchment paper the same size as your baking sheets and use a 2-inch cookie cutter to draw 10 2-inch circles on it, making sure to leave some space between each one (this will be your template for piping the dough). Line two large baking sheets with parchment paper and set aside.
Combine water, sliced butter, sugar, and salt in a large saucepan. Place the saucepan over medium heat and bring to a boil, stirring occasionally.
Stir in the cup of flour with a wooden spoon until fully combined. Keep the mixture over medium heat and continue stirring until the mixture pulls away from the sides of the pan, forms a smooth dough, and leaves a film on the bottom of the pan (about 2 to 3 minutes).
Remove the mixture from the heat and transfer it to a large heat-proof bowl to cool slightly for 3 minutes.
Mix in the eggs, one at a time, with a wooden spoon or an electric mixer, making sure to mix in each one until fully combined before adding the next. Once the 4th egg is fully mixed in, the dough should hold a V-shape on the end of the spoon or beaters.
Transfer the dough to a large piping bag fitted with a ½-inch round piping tip (I use the Wilton 1A tip).
Place the template underneath the parchment paper on one of your prepared baking sheets. Place the piping bag perpendicular to the parchment paper about ½-inch above it, this will ensure that the cream puffs rise straight up. Applying even pressure, pipe 2-inch circles, letting them expand in both height and width, and making sure to swirl the tip when you are done (do not pull straight up). Remove the template beneath the parchment paper and repeat with the other baking baking sheet, you should end up with 18 to 20 circles total.
Dip your finger in a little water and gently smooth out any pointed peaks.
To make the egg wash: In a small mixing bowl, whisk the egg and water together until fully combined. Gently brush the top of each one with the egg wash.
Bake for 30 to 35 minutes or until the cream puffs are golden brown, making sure not to open the oven door as they are baking. Once they’re done, turn the oven off, remove them from the oven, use a knife or skewer to pierce a hole in the side of each one, then return to the oven with the door cracked open for 10 minutes.
Remove from the oven and carefully transfer to a wire rack to cool completely. Once cooled fill with whipped cream, pastry cream, or your favorite filling.