How to Make It
In a medium heatproof bowl, combine the chocolate and boiling water and stir until completely melted and smooth. Refrigerate the filling until firm, at least 1 hour and as long as overnight.
Preheat the oven to 350°. Brush six 4-ounce ramekins with the melted butter. Line the bottoms with rounds of wax paper, butter the paper and sprinkle with sugar.
In a large bowl, beat the eggs and the 6 tablespoons of sugar with an electric mixer until pale and thick. Sift the cocoa powder, flour and star anise into a bowl. Whisk in the half-and-half and rum just until smooth. Lightly whisk in the beaten egg mixture.
Moisten 1 cup of frozen brioche cubes at a time in the chocolate custard until slightly saturated, about 30 seconds. Using a slotted spoon, drain the brioche cubes and use them to fill the ramekins halfway. Place 1 1/2 tablespoons of the chocolate filling in the center of each ramekin. Moisten the remaining frozen brioche cubes in batches and fill the ramekins, mounding them slightly in the center. Discard any remaining chocolate custard.
Set the ramekins in a roasting pan and pour enough hot water into the pan to reach 1 inch up the sides. Cover the pan with foil and bake for about 25 minutes, or until the puddings are puffed and set. Remove the ramekins from the water bath and let cool for 10 minutes before unmolding.
Invert the bread puddings onto small dessert plates. Remove the wax paper and serve warm with the sweetened whipped cream.
Ground star anise is available at specialty food shops.