In a saucepan over medium-high heat, melt butter then add water, salt, vanilla, and cinnamon stick. Bring to a boil then remove the cinnamon stick and remove the mixture from heat.
Add the flour and stir with a wooden spoon until a smooth dough is formed, about 3-5 minutes.
Let dough cool, about 10-15 minutes then transfer to a bowl and add the egg. Stir vigorously until egg is incorporated. The mixture is pretty hot so you have to stir vigorously so the egg doesn't actually cook and you get scrambled eggs :)