Heat the oven to 350°F.  While the oven is heating, lightly grease a 3-quart shallow baking dish.  Mash 1 banana in a bowl with a fork.  Cut the remaining banana into slices.
Place the bread pieces and chocolate pieces into the baking dish.  Beat the mashed banana, milk, eggs, brown sugar and vanilla extract in a medium bowl with a fork or whisk.  Pour the milk mixture over the bread mixture.  Stir and press the bread mixture into the milk mixture to coat.  Top with the sliced banana.  Cover and refrigerate for 1 hour or overnight.
Bake for 55 minutes or until a knife inserted in the center comes out clean.