Preheat oven to 425°F/218°C.
Line a large baking sheet with parchment paper.
In a small sauce pot, bring water to a boil, add in the butter and stir to melt.
Once the butter has melted, remove the pot from heat and dump in the flour at once.
Quickly stir the mixture with a wooden spoon until it forms a ball of dough.
Transfer the dough over to a stand mixer fitted with a paddle.
Cool down the dough by running the mixer on low speed, about 3-5 minutes.
Gradually add in the beaten egg, until the dough is glossy and smooth. Make sure to just add enough egg. You may not need the entire amount. Test to see if the batter holds a "v" shape when you pull the paddle straight up.
Transfer the choux dough to a piping bag fitted with a large piping tip, or just cut off the tip of the bag.
You'll want a pretty substantial opening for piping the choux.
Pipe 4 round rings about 8cm in diameter onto the parchment-lined baking sheet. Space the rings apart.
If there are any "tails" from the dough that pop up, you can use a slightly wet finger (dipped in water) to pat them down.
Bake at 425°F/218°C for 10 minutes, and then reduce to 350°F/177°C for another 20 minutes, until golden.
Turn off the heat. Remove the choux nuts from the oven, turn them over and poke 4 holes on the bottom using a skewer (to let the interior dry out).
Return the choux nuts to the oven for an additional 5 minutes.
Remove from oven and let cool completely on a wire rack.