•2 1/2 cups (350 grams) unbleached all-purpose flour, plus more if needed
•2 1/4 cups (340 grams) bread flour
•1 1/2 packages (3 1/4 teaspoons) active dry yeast or 1-ounce (28 grams) fresh cake yeast
•1/3 cup plus 1 tablespoon (82 grams) sugar
•1 tablespoon kosher salt
•1/2 cup cold water
•6 eggs (1 for the egg wash)
•1 3/8 cups (2 3/4 sticks; 310 grams) unsalted butter, at room temperature, cut into 10 to 12 pieces
•2 bars of chocolate, 4 oz. each (60-70% cocoa)
Using a stand mixer fitted with the dough hook, combine the all-purpose flour, bread flour, yeast, sugar, salt, water, and 5 of the eggs. Beat on low speed for 3 to 4 minutes, or until all the ingredients are combined. Stop the mixer, as needed, to scrape the sides and bottom of the bowl to make sure all the flour is incorporated into the wet ingredients. Once the dough has come together, beat on low speed for another 3 to 4 minutes. The dough will be very stiff and seem quite dry.
With the mixer on low speed, add the butter, 1 piece at a time, mixing after each addition until it disappears into the dough. Continue mixing on low speed for about 10 minutes, stopping the mixer occasionally to scrape the sides and bottom of the bowl. It is important for all the butter to be thoroughly mixed into the dough. If necessary, stop the mixer occasionally and break up the dough with your hands to help mix in the butter.
Once the butter is completely incorporated, turn up the speed to medium and beat until the dough becomes sticky, soft, and somewhat shiny, another 15 minutes. It will take some time to come together. It will look shaggy and questionable at the start and then eventually it will turn smooth and silky. Turn the speed to medium-high and beat for about 1 minute. You should hear the dough make a slap-slap-slap sound as it hits the sides of the bowl. Test the dough by pulling at it; it should stretch a bit and have a little give. If it seems wet and loose and more like a batter than a dough, add a few tablespoons of flour and mix until it comes together. If it breaks off into pieces when you pull at it, continue to mix on medium speed for another 2 to 3 minutes, or until it develops more strength and stretches when you grab it. It is ready when you can gather it all together and pick it up in 1 piece.
Put the dough in a large bowl or plastic container and cover it with plastic wrap, pressing the wrap directly onto the surface of the dough. Let the dough proof (that is, grow and develop flavor) in the refrigerator for at least 6 hours or up to overnight At this point you can freeze the dough in an airtight container for up to 1 week.
To assemble & finish:
Line a baking sheet with parchment paper.
On a floured work surface, roll out the dough into a rectangle about 20 inches by 10 inches and 1/4 inch thick. It will have the consistency of cold, damp Play-Doh and should be fairly easy to roll. Position the rectangle so a long side is facing you. Take your chocolate and cut it up into small chunks, sprinkle onto the top half of the dough. Fold the top half of the rectangle completely over the bottom half, then press down gently so the halves are smooshed together.
Use a bench scraper of a chef’s knife to cut the filled dough into 10 pieces, each about 2 inches wide; each piece will be about 2 by 5 inches. (At this point, the unbaked pastries can be tightly wrapped in plastic and frozen for up to 1 week. When ready to bake, thaw them, still wrapped, in the refrigerator overnight or at room temperature for 2 to 3 hours, then proceed as directed.)
Carefully transfer the brioche to the prepared baking sheet. Cover the pastries lightly with plastic wrap and place in a warm spot to proof for about 2 hours, or until the dough is puffy, pillowy, and soft. Position a rack in the center of the oven, and heat the oven to 350 degrees F.
In a small bowl, whisk the egg until blended. Gently brush the tops of the pastries with the beaten egg.
Bake for 35 to 45 minutes, or until golden brown. Let cool on the baking sheet on a wire rack for 20 to 30 minutes. The pastries tend to bake into one another in the oven, so break apart into 10 pieces. The pastries are best served warm or within 4 hours of baking. They can be stored in an airtight container at room temperature for up to 1 day, and then warmed in a 300-degree-F oven for 5 minutes before serving.