- Start by making the dough: mix the yeast, salt, eggs, honey and melted butter with the water in a 5-quart (4.7 liter) bowl or lidded (not airtight) food container. Mix in the flour without kneading, using a spoon. You can also use a 14-cup capacity food processor or a heavy-duty stand mixer with dough hook. If you're not using a machine, you may need to use wet hands to incorporate the last bit of flour. The dough will be loose but will firm up when chilled. Don't try to work with it before chilling. You may notice lumps in the dough but they will disappear in the finished product.
- Cover (not airtight) and allow to rest at room temperature until dough rises and collapses (or flattens on top), approximately 2 hours.
- The dough can be used as soon as it's chilled after the initial rise. Refrigerate in a lidded (not airtight) container and use over the next 5 days. Beyond 5 days, freeze the dough in 1-pound (450 grams) portions in an airtight container for up to 4 weeks. When using frozen dough, thaw in the refrigerator for 24 hours before using, then allow the usual rise and rest times.
- Now, make the ganache: melt the chocolate over a double boiler or in the microwave on low, until smooth. Remove from heat, add the butter and stir until incorporated.
- Stir the cocoa into the rum, add the corn syrup and mix until smooth. Add to the chocolate and butter mixture.
- Lightly butter a 9x4x3-inch nonstick loaf pan (I used a regular 26x10x5 centimeter pan lined with baking paper). Dust the surface of the refrigerated dough with flour and cut off a 1-pound (450 gram/grapefruit-sized) piece. Dust the piece with more flour and quickly shape in into a ball by stretching the surface of the dough around to the bottom on all four sides, rotating the ball a quarter turn as you go. Using a rolling pin, roll out the ball into a 1/4-inch (0.60 centimeter) thick rectangle, dusting with flour as needed.
- Spread 1/2 cup of the ganache evenly over the rectangle, leaving a 1-inch (2.5 centimeter) border all around. Starting at the short end, roll up the dough, being careful to seal the bare edges. Gently tuck the loose ends underneath, elongate into an oval and drop into the prepared pan. Allow to rest 1 hour and 40 minutes.
- Preheat the oven to 180ÂºC/350ÂºF. Using a pastry brush, paint the top crust with the egg white. Sprinkle lightly with granulated sugar.
- Bake the brioche for about 45 minutes or until the top is golden brown and the sugar caramelizes. Remove from the pan and cool slightly, then drizzle the remaining 1/4 cup ganache over the top crust. Cool completely and slice.