1 cup plus 3 tablespoons sugar, plus more for the baking dish
2 cups milk
2 cups heavy cream
1 pound brioche, crusts trimmed, bread cut into 3-inch chunks
2 sticks ( 1/2 pound) unsalted butter, softened
8 large egg yolks, at room temperature
3 very ripe large bananas, mashed
4 large egg whites, at room temperature
1 cup best-quality store-bought fudge sauce, plus more for serving
Butterscotch sauce, for serving
Preheat the oven to 350°. Butter a 4-quart glass or ceramic baking dish and coat with sugar, tapping out any excess.
In a saucepan, combine the milk with the cream and bring just to a simmer. Put the brioche in a large bowl, pour the milk evenly over it and let stand until nearly absorbed, stirring once or twice.
In a medium bowl, beat the butter until creamy. Add 1 cup of the sugar; beat until fluffy. Beat in the egg yolks, 1 at a time. Fold the mixture into the soaked brioche, then stir in the bananas.
In a clean bowl, whip the egg whites to soft peaks. Gradually add 2 tablespoons of the sugar and beat until the whites are stiff and glossy, about 2 minutes. Fold the whites into the pudding.
Transfer the pudding to the prepared baking dish; smooth the surface. Dollop spoonfuls of the fudge sauce over the top and swirl it into the pudding. Sprinkle the top with the remaining 1 tablespoon of sugar. Set the baking dish in a large roasting pan and add enough hot water to reach two-thirds of the way up the side. Bake for 1 hour, or until the pudding is set and the top is brown.
Cool the pudding slightly in the water. Transfer to a rack to cool for 15 minutes. Serve with fudge and butterscotch sauce.