Preheat oven to 400°F.
In a small pot, heat the butter, water, and milk on medium heat until it comes to a simmer.
Pour all the flour into the pot and quickly stir with a spatula until a dough forms.
Keep flattening and moving the dough around the bottom of the pot on medium heat to dry it out (about 4 minutes). The dough should resemble mashed potatoes. Remove pot from heat.
Cool the dough for 5-10 minutes until it is barely warm to the touch.
Add the egg to the choux dough a third at a time, stirring between each addition. It will look curdled at first but just keep stirring and adding the rest of the egg. The dough is at the right consistency when you drop it from the spatula and the dough leaves a V-shape hanging off the spatula.
Transfer the choux dough to a piping bag and snip off the tip of the bag to create a ½ inch opening.
On a baking sheet lined with parchment paper, pipe dollops about 1 inch in diameter and 1 inch tall. Leave at least 3 inches in between each dollop for when the choux inflates (about 6 on each baking sheet).
Take the frozen craquelin sheet of the freezer and use a 2 inch round cutter to cut discs out. Place one disc on top of each dollop of choux batter.
Bake at 400°F for 5 minutes. Turn down the temperature to 350°F and bake for another 25-30 minutes. About 2 minutes before the puffs are done baking, use a chopstick to poke a hole in each puff to release the steam. Bake until the puffs are browned on top and walls are stiff. Cool completely before filling.