Mix the Dough: Weigh the flour, or measure it by gently spooning it into a measuring cup and sweeping off the excess. Place all the dough ingredients in a stand mixer or bread machine and mix until a smooth, shiny dough forms. The dough will initially be very sticky, but continued kneading will develop it into a satiny dough. Knead Thoroughly: If using a stand mixer, knead the dough for up to 15 minutes because brioche requires longer development than many other doughs. If using a bread machine, use the dough cycle. The dough is very sticky, so hand kneading is not recommended. Add Chocolate and Cherries: If using a bread machine, add the chocolate and dried cherries about 1 minute before the kneading cycle ends. If using a stand mixer, incorporate the chocolate and cherries at the end of kneading. First Rise and Refrigeration: For stand-mixer dough, shape the soft dough into a ball, place it in a greased bowl, cover, and let it rise for 1 hour. For bread-machine dough, allow the complete dough cycle to finish.Then cover the dough with plastic wrap and refrigerate it for several hours or overnight. Refrigeration slows fermentation and chills the butter, making the dough easier to shape. Prepare the Dough: Remove the chilled dough from the refrigerator and transfer it to a lightly floured work surface.
Shape the Dough: Form the dough into a log approximately 24 inches long. Flatten the log until it is about 6 to 7 inches wide. It does not need to be perfectly even; the flattened dough may look somewhat ragged. Prepare the Cocoa Filling: Whisk the confectioners' sugar and Dutch-process cocoa together until evenly combined.
Fill the Dough: Lightly brush the flattened dough with milk or water, then distribute the confectioners' sugar and cocoa mixture evenly over its surface.
Roll the Dough: Starting from one long edge, roll the dough into a long log, keeping the filling enclosed inside.
Shape the Brioche: Place the filled log into a lightly greased 9-inch round cake pan that is at least 2 inches tall. Coil the log inside the pan or shape it into a circle, then pinch the two ends together to close the ring. Proof the Brioche: Cover the pan and let the shaped brioche rise for 2 to 3 hours, until it looks quite puffy. Toward the end of this rising period, preheat the oven to 350°F. Apply the Topping: Lightly beat the reserved egg white with 1 tablespoon cold water.Brush it over the risen brioche, then sprinkle the surface with 2 to 3 tablespoons of pearl sugar or coarse sparkling sugar. Bake the Brioche: Bake the brioche at 350°F for 20 minutes.
Protect the Crust: After the first 20 minutes of baking, tent the brioche loosely with aluminum foil. Continue baking for another 30 to 35 minutes, until the brioche is golden brown and the interior reaches 190°F on an instant-read thermometer. Cool the Brioche: Remove the brioche from the oven and let it rest for about 5 minutes. Loosen the edges carefully, then turn the brioche out of the pan onto a wire rack to cool.
