Preheat oven 350°F/180°C.
Grease a glass baking dish with butter.
In a large bowl, whisk together eggs, milk, heavy cream, and sugar.
Add bread to the bowl and mix until bread is completely coated with the liquid.
Allow bread to soak for at least 30 minutes.
Fold mashed banana and chocolate into the bread mixture.
Pour bread mixture into a prepared baking dish.
Bake for 30 to 40 minutes, or until golden brown and set.
Sprinkle chopped walnuts.
Let it cool and serve at room temperature.