In a stand mixer fitted with a dough hook, add water, milk, sugar, yeast, flour, salt, and butter. Mix on low until dough forms and knead for 5 minutes.

Knead briefly by hand, then place dough in a covered bowl and let rise for 1–2 hours until just doubled.

Flatten dough, wrap, and chill in freezer for 15 minutes.

Mix butter and flour until smooth. Roll dough to a 10×20-inch rectangle and spread butter over the bottom 3/4.

Fold dough over butter in sections, rotate, and roll to an 8×20-inch rectangle. Fold into thirds like a letter.

Wrap and refrigerate for 2 hours.

Roll dough to 10×18 inches, trim edges, and cut into twelve 3×5-inch rectangles.

Place chocolate batons inside each rectangle, fold tightly, and seal.

Proof croissants on lined baking sheets for 2–4 hours until puffy and jiggly.

Brush with egg wash, spritz parchment lightly with water, and bake at 375°F (190°C) for 24–26 minutes until golden.