Preheat oven to 350 degrees F. Grease a 2-quart baking pan, and set pan into a larger pan. Add water to the larger pan, preparing a water bath in which the pudding will bake.
In a large bowl, whisk together eggs and sugar. Whisk in milk, cream and vanilla. Transfer 1 cup of this custard mixture to a saucepan and set aside.
Add stollen and chocolate to remaining custard mixture in the large bowl; stir well. Pour into prepared baking pan and bake until puffed and firm in the center, about 1 1/4 hours.
Meanwhile, add pear brandy to reserved custard mixture and heat on medium-low, whisking constantly, until it thickens and coats the back of a spoon. (Be careful not to turn the heat too high or stop whisking, as the eggs might scramble.)
Remove pudding from oven and let cool before slicing. Meanwhile, prepare Caramelized Bananas. To serve, place a few warm banana slices on each plate, top with a square of warm bread pudding, and drizzle with warm custard sauce.