Cube your butter into chunks and make sure it is soft to the touch before you proceed.
From the dough mix ingredients, combine the hot water and cocoa powder together and whisk to make a slurry.
In a mixing bowl (either standing mixer with dough hook, or if hand mixing a large mixing bowl), combine the rest of the ingredients, except for half of the butter and the salt, but including the slurry.
If you are machine mixing, start at the lowest speed and mix for 2 minutes. Crank the machine up to medium speed and mix for 2-3 minutes or until you see the dough start to come together. Let the dough rest for 1 minute, and then add the rest of your butter and the salt before switching it to the highest speed setting and let it mix until the dough slaps on the side of the bowl and has a smooth surface. This can take 10-15 minutes.
If you are hand mixing, first add only half of the butter and squeeze until all ingredients are incorporated. Once you have a consistent texture, you can begin to stretch and slap the dough on the table, while slowly incorporating the rest of the butter. It will come apart very easily, but the longer you knead/stretch/slap the dough, the more it will come together. You can give it a few periods of rest (5 or so minutes) to let it come together.
Remember: with a machine mix, it takes 15 or so minutes for the dough to come together. If you opt to hand mix brioche, be prepared to knead and develop your dough for at least 30 minutes. Flour your work surface as well, to ensure that your dough doesn't stick too much.
Once your dough is fairly smooth on the surface and has come together, place it in a clean and oiled bowl for bulk fermentation. If you hand-mixed, you can give it a couple of stretches and folds every 30 minutes to continue to help the gluten formation process.
Allow your dough to go through the initial rise in a warm place for 4 hours. My house temperature is usually between 72-75f.
While the dough is fermenting, make the dough filling. Melt the chocolate and butter together either using a double boiler or directly in the microwave.
Add the powdered sugar and cocoa powder and mix tother until a thick paste forms. Set aside.
After you notice your dough is smooth and springy to the touch, lightly flour your work surface and dump dump the dough out onto it. Without using a rolling pin, stretch the dough into a rectangle thats about 12 x 18 (give or take). If you don't have an extra long loaf pan, then divide the dough in two to make two separate iterations as follows.
Crumble the filling all over the surface of the dough and then lightly pat it into the dough. Make sure you distribute it as evenly as possible. Fold the dough in thirds like a book, from the shorter sides. Use a rolling pin to roll the dough out, making sure to stretch it out on the longer sides.
Using a pizza cutting wheel or a large knife, divide the dough into 3 long strips. Twist the long strips and then combine them at the bottom tips and make a simple three strand braid.
Proof in a warm, covered space for about 2 hours, or until the dough grows noticeably in size and becomes springy to the touch. You'll also start to get a great aroma from the dough.
Preheat your oven to 375f, and egg wash your brioche.
Bake your chocolate brioche for 35-40 minutes. Depending on your oven and color preference you may need to go a bit longer.
