1. To make the dough, in a large mixing bowl with dough hook attachment, combine all the ingredients for the dough and mix until the dough comes together, about 5 minutes. Transfer the dough onto floured surface and knead for a minute. Flatten it into a disk and place it in the floured dish. (I use 8x8-inch baking pan.) Cover with plastic wrap and refrigerate for at least 6 hours, or overnight.
2. To prepare the butter, cut the butter sticks lengthwise and put them on a large parchment paper. Place another large parchment paper over the butter and roll it into 7x7-inch square. Trim the edges and place them over the butter and roll again until you get nice and even flat square of butter. Refrigerate for at least 30 minutes, or overnight. Do NOT freeze. (Frozen butter doesn’t soften easily during laminating process, and it’ll only lead to frustration. Refrigerating for at least 30 minutes will do the trick.)
3. To make the layers (laminating process), roll the chilled dough on a floured surface into a 10x10-inch square. (It doesn’t have to be exact, but close enough.)
4. Place the prepared square butter in the middle of the dough so that corners of butter are pointing to the middle of sides of the dough. Fold the edges like an envelop and pinch the seams securely. (See picture in this post.
5. Roll the dough into 8x24-inch rectangle. Again, it doesn’t have to be exact measurements, but do your best to be close to that. Fold into thirds and cover with plastic wrap. Refrigerate for 30 minutes.
6. Repeat step 5 two more times with 30-minute rest in the fridge in between. If the dough resist too much at any point, refrigerate for 10-15 minutes.
7. After 3rd rolling, fold the dough again into thirds, cover with plastic wrap and refrigerate overnight, or at least 8 hours.
8. Cut the dough into 2 equal parts and roll each one into 8x22-inch rectangle. Make sure to lift the dough before final measurement, because it shrinks back a little.
9. Using a sharp knife, cut each dough into 4 rectangles. You should get 8 rectangles total.
10. Place 1 piece of chocolate on one edge, and the 2nd piece in the middle of rectangle. Starting with chocolate edge, roll the dough tightly. Place it on a baking sheet, lined with parchment paper, or silicone mat. 4 pain au chocolat per baking sheet with ample space in between.
11. Cover with plastic wrap and rest for about an hour, or until doubled in size.
12. Preheat the oven to 425°F (220°C).
13. Right before baking, beat egg yolk with 1 tablespoon of water in a small bowl. Brush the egg wash over the croissants.
14. Bake for 20-25 minutes, until golden brown. Serve warm.