1) In a stand mixer or in a bread machine, mix together all of the ingredients to form a smooth, shiny dough. Don't worry; what starts out as a sticky mess becomes beautifully satiny as it kneads. If you use a stand mixer, this dough takes longer than most to develop, so be prepared to let it knead for up to 15 minutes. A bread machine will mix and knead this dough perfectly using the dough cycle. We don't recommend trying to knead brioche dough by hand; it's simply too sticky.
2) If you're using a bread machine, add the chocolate chunks and dried cherries about 1 minute before the end of the kneading cycle. Let it complete its entire dough cycle, then cover the bucket with plastic wrap, and refrigerate the dough for several hours, or overnight. If you've kneaded the dough in a stand mixer, add the cherries and chocolate at the end, form it into a ball (it'll be very soft), place it in a greased bowl, cover the bowl, and it let rise for 1 hour. Then refrigerate the dough for several hours, or overnight. Refrigeration will slow the fermentation and chill the butter, making the dough easier to shape.
3) Remove the dough from the refrigerator, and place it on a lightly floured work surface.
4) Shape the dough into a 24" log. Flatten it out so it's about 6" to 7" wide. Don't try to make it perfectly even; it'll look ragged.
5) Make the filling by whisking together the confectioners' sugar and cocoa. Brush the dough with milk or water, and sprinkle the sugar/cocoa filling evenly over the dough. Starting with a long end, roll the dough into a long log.
6) Lay the log in a lightly greased 9" round cake pan that's at least 2" tall. You can coil it into the pan, or simply make it into a circle. Pinch the dough together where the ends meet.
7) Cover the pan, and allow the brioche to rise for 2 to 3 hours, till it's quite puffy. Towards the end of the rising time, preheat the oven to 350°F.
8) Brush the risen brioche with the beaten egg white, and sprinkle with the pearl sugar or coarse white sugar.
9) Bake the brioche for 20 minutes. Tent it with aluminum foil, and bake for an additional 30 to 35 minutes, until it's golden brown and its interior registers 190°F on an instant-read thermometer.
10) Remove the brioche from the oven, and after about 5 minutes loosen the edges, and carefully turn it out of the pan onto a rack to cool.
Yield: one 9" brioche.