Preheat the oven to 180˚C and line a baking sheet with parchment paper. Using the same cookie cutter as you did for the craquelin, trace 12 circles on the baking sheet, leaving about 2-inches between each. Flip the baking sheet over so the drawings are on the underneath. Set aside.
Fit a large piping bag with a large round piping tip. Set aside.
In a medium pot, combine the milk, water, butter, vanilla extract, and sugar. Place the mixture over a medium heat & stir continuously until the butter has melted & the mixture has begun to boil. Remove the pot from the heat & add the flour all at once, mixing quickly with a wooden spoon into a thick paste.
Return to the heat, and, stirring constantly, cook the mixture for 2 minutes to help dry it out – there will be a fine layer on the bottom of the pot when it’s ready. Transfer choux dough to the bowl of a stand mixer fitted with the paddle attachment & mix on medium speed for 1 minute to help cool down.
With the mixture running on low, slowly stream in the eggs. Mix on medium speed for 4 minutes, or until the egg is fully incorporated. The batter is ready when you dip the paddle into the mixture and it forms a v before breaking off.
Transfer the choux to the prepared piping bag & pipe out 12 circles onto the parchment. Flatten down with any points of dough with a damp fingertip.
Remove the craquelin from the freezer & carefully place each on top of a mound of choux.
Bake the puffs for 35 minutes at 180˚C, then turn the oven to 160˚C, and bake for a further 10 minutes, until deeply golden in colour. Remove from the oven and poke a small hole in the side of each – I used a chopstick. Place on a cooling rack to cool completely.