Cook the Dough: Add the water, milk, flour, sugar, and butter to a large pot. Cook over medium heat, stirring constantly, until a smooth dough forms, pulls away cleanly from the sides and bottom of the pot, and no longer looks wet.
Cool Slightly: Remove the dough from the heat and let it cool for a few minutes. It should still be warm, but not hot enough to cook the eggs.
Add the Eggs: Transfer the dough to a stand mixer and mix on low speed. Add the eggs one at a time, allowing each egg to become completely incorporated before adding the next.
Mix Until Smooth: Continue mixing until the dough is smooth, uniform, and soft enough to pipe.
Pipe: Transfer the dough to a piping bag fitted with a large star tip and pipe the churros into your desired length.
Fry: Fry the churros in hot oil until golden on the outside and cooked through.
Drain: Transfer the churros to a paper towel-lined tray or cooling rack and let the excess oil drain.
Fill: Once the churros are cool enough to handle, fill them with the 120 g dulce de leche, dividing it between approximately 15 churros.