Preheat the oven to 170°C (338°F).
In a saucepan, heat the water, milk, butter, salt, and sugar until the butter melts and the mixture boils.
Remove from heat and quickly stir in the flour. Return to low heat and cook the dough for 2-3 minutes, stirring constantly, to dry it out.
Let the dough cool slightly, then transfer it to a food processor. Gradually add the beaten eggs until a smooth dough forms.
Pipe the dough into circles (for Paris-Brest) on a lined baking sheet, then place the pre-cut craquelin on top.
Bake for 35-40 minutes until golden brown. Let the choux buns cool completely.