Bring the milk, butter, water, and sugar to a boil in a medium saucepan, about 2 minutes. When the mixture reaches a rolling boil, add the flour all at once, and stir quickly until the resulting dough pulls from the sides of the pan. Stir for another minute.
Add the dough to a stand mixer and let the dough cool for 3 minutes. Turn the mixer on low, then add the eggs one at a time. The dough should be smooth and thick.
Preheat the oven to 425°F. Line 2 baking sheets with parchment.
Transfer the dough to a piping bag and pipe into 1 1/2-inch dollops, about a 1/2-inch tall, onto the prepared baking sheets. Leave about 2 inches between the puffs.
Remove the craquelin from the freezer. Cut the dough into circles with a cookie cutter. It should be about the same size as the puff. Add the frozen disks to the tops of each puff.
Bake in the preheated oven for 20 minutes, rotate pans and bake for another 10 to 15 minutes, until golden.
Allow to cool completely on the baking sheet placed on a wire rack, about 30 minutes.
Slice the puffs in half and fill with the ice cream. Drizzle with chocolate sauce.