In the bowl of a stand mixer (or by hand), combine water, milk, yeast, sugar, bread flour, salt and the 4 Tbsp softened butter. Mix on low until a dough forms, then knead about 5 minutes until smooth and slightly elastic.

Shape into a rough rectangle, wrap and chill ~15 minutes in freezer. Meanwhile, mix chilled butter cubes with ¼ cup flour to form a butter block.

Enclose butter block inside dough, then laminate by rolling and folding per shortcut or classic method. This recipe uses one streamlined lamination step to produce layered dough more quickly.

After folding, chill and allow dough to rest/proof for ~4 to 4½ hours, or longer if following an overnight plan.

Roll dough into a rectangle and cut into rectangles. Place chocolate batons or a few strips of chopped chocolate at one end of each, then roll up into pain au chocolat shapes.

Arrange on parchment‑lined baking sheets, leaving space to proof. Let rise for about 2–3 hours in a warm, humid environment (cover with plastic and/or inside a plastic-lined tent) until puffy and jiggly.

Preheat oven to high (around 425–450 °F / 220–230 °C). Just before baking, brush with egg wash and mist baking tray with water or spritz inside oven for steam to encourage oven-spring.

Bake for 20–24 minutes until deeply golden, rotating trays halfway and optionally brushing again with melted butter or egg wash.

Cool briefly (about 10 minutes), dust with confectioners’ sugar if desired, and serve warm or at room temperature.