1. Make the Dough:

   • In a large bowl, combine flour, sugar, salt, and instant yeast. Mix well.
   • Slowly add the lukewarm milk, stirring until the dough comes together. Knead for about 5 minutes until smooth.
   • Shape the dough into a ball, cover with plastic wrap, and refrigerate for at least 1 hour.

2. Prepare the Butter Block:

   • Place the cold butter between two sheets of parchment paper. Use a rolling pin to flatten it into a rectangle about 1/2 inch thick (approximately 8×10 inches).
   • Chill the butter block in the refrigerator while the dough rests.

3. Incorporate the Butter:

   • On a lightly floured surface, roll the chilled dough into a rectangle (about 12×20 inches). Place the butter block in the center of the dough.
   • Fold the dough over the butter, sealing the edges to enclose it completely.

4. Roll and Fold:

   • Roll the dough into a long rectangle (about 12×24 inches). Fold it into thirds like a letter (this is called a “turn”). Wrap it in plastic wrap and refrigerate for 30 minutes.
   • Repeat this rolling and folding process two more times (total of three turns), chilling the dough for 30 minutes between each turn.

5. Shape the Pastries:

   • After the final chill, roll the dough into a rectangle (about 12×20 inches). Cut it into 8 equal rectangles.
   • Place a piece of dark chocolate on one edge of each rectangle, then roll the dough around the chocolate to form a log shape. Seal the edges by pressing them together.

6. Proof:

   • Place the rolled pastries seam-side down on a baking sheet lined with parchment paper. Cover with a kitchen towel and let them rise in a warm place for about 1-2 hours, or until they have doubled in size.

7. Preheat the Oven:

   • Preheat your oven to 400°F (200°C).

8. Egg Wash:

   • Beat the egg in a small bowl and brush the tops of the pastries with the egg wash for a golden finish.

9. Bake:

   • Bake in the preheated oven for 20-25 minutes, or until the pastries are puffed and golden brown.

10. Cool and Serve:

    • Allow the pain au chocolat to cool slightly on a wire rack before serving. Enjoy them warm or at room temperature.

Serving Suggestions:

Serve pain au chocolat with a cup of coffee or hot chocolate for a classic French breakfast or snack. They can also be enjoyed fresh out of the oven or reheated for a few minutes to restore their flakiness.