Place the warm water in the bowl of a stand mixer fitted with the hook attachment. Whisk in the yeast and let it dissolve and bloom for 10 minutes.
½ cup water, 1½ teaspoons active dry yeast
Add the flour, 3 tablespoons of butter, sugar, and salt. Mix on low speed, scraping the sides of the bowl as needed until a rough dough is formed. Turn up the speed to medium and knead for 3-4 minutes until a smooth dough ball forms.
1 ¾ cups all-purpose flour, 3 tablespoons unsalted butter, 2 tablespoons granulated sugar, 1 teaspoon kosher salt
With floured hands, gather up the dough and mold it into a semi-smooth ball. Place the dough back in the mixer bowl, cover it with a kitchen towel or plastic wrap, and let it rise in a warm place for 2 hours, until it has doubled in size.
Transfer the risen dough to a lightly floured work surface and press down to deflate it. Stretch it into a 12x8-inch rectangle. Fold it into thirds, wrap it in plastic wrap, and chill it on a baking sheet in the refrigerator for 1 hour.
Cut the 1¼ cups of butter into ½-inch slices (lengthwise if using stick butter). Place the pieces slightly apart from each other on a large piece of parchment paper. Lay another piece of parchment over the butter. Press the butter down with a rolling pin into an even layer, then roll it into an 8x8-inch square. Trim any jagged edges and place the trimmings back on top of the butter and continue to roll into a square. Refrigerate until a little chilled and just barely flexible, 10 or 15 minutes.
1¼ cups unsalted butter
Remove the dough from the refrigerator and transfer it to a lightly floured surface. Roll the dough into a 17x9-inch rectangle.
Place the butter layer on one half of the dough, leaving about 1 inch margin from the edge of the dough. Fold the other half of the dough over the butter, and roll the rolling pin over to seal the edges, dusting your work surface and the dough with flour as needed.
Press the rolling pin down on the dough to create ridges, then roll them out. Repeat as needed until you again have a 12x8-inch rectangle.
Starting from the short side, fold one-third of the dough over the middle third. Then fold the other end over to form a small rectangle. Flatten it out slightly with the rolling pin, then transfer it back to the baking sheet. Cover it with plastic wrap and refrigerate for 1 hour.
Repeat steps 8 and 9 two more times, chilling the dough for 1 hour between each turn, or overnight after the third turn.
Place the dough on a lightly dusted work surface. Cut the rectangle in half and return one of the halves to the refrigerator to chill while you work the other. Roll the dough to a 16x8-inch rectangle, using as little flour as needed to keep the dough from sticking, then use a pizza cutter to cut it into 4 pieces, about ¼-inch thick.
Pull the corners of one piece gently, stretching the ends out to a slight taper. Line 1-2 tablespoons of chocolate about 1 inch parallel to the bottom edge, and another 1-2 tablespoons 1 more inch ahead, about in the middle of the rectangle.
8 ounces sweetened chocolate bars
Roll the dough up over the chocolate toward the other edge to form a cylinder. Place the rolled croissants on 2 parchment-lined baking sheets with the seam at the bottom.
Whisk together the egg and 1 tablespoon water and brush the croissants twice with the egg wash. Place the pans in a warm area to rise for 1-2 hours. Place the remaining egg wash in the refrigerator.
1 large egg
Preheat oven to 400°F. Brush the proofed croissants gently with the rest of the egg wash. Bake for 15-20 minutes, turning the pans once, until dark golden brown. Allow them to cool a bit before serving.