Preheat oven to 325 degrees.
Butter a 13x9x2 inch baking dish.
Whisk the eggs, and sugar in a large bowl and blend well. Whisk in the cream, bourbon, vanilla and salt. Add brioche cubes to egg and cream mixture. Mix thoroughly to moisten and let sit for 1 hour, stirring every so often.
While mixture is soaking, combine bittersweet chocolate chips and cocoa powder, coating every chip with the cocoa.
Pour bread mixture into prepared baking dish. Carefully stir in the chocolate chips to evenly distribute.
Bake until the pudding turns deep golden brown, is beginning to rise up the sides of the dish, and is slightly jiggly in the center. This will take about 50 minutes. Remove from the oven and cool slightly.