Add the milk, heavy cream, eggs, sugar, and vanilla to a blender and blend to combine or use a whisk and a mixing bowl to mix together.
Spray a 9x13 baking dish or 2.5 quart casserole dish with nonstick spray and spread half of the banana bread cubes along the bottom of the dish in a single layer then top with half of the banana slices. Pour half of the egg mixture over the banana bread mixture. Banana bread that has been slightly dried out works best to keep the pudding from becoming soggy. If your banana bread is too moist, place in an oven set at 200 degrees for 20 minutes, then allow to cool.
Place the rest of the banana bread cubes and banana slices in the dish and pour the remaining cream mixture over the top. Allow the banana bread to rest in the dish for 10 minutes to soak up the mixture.
Bake at 350 degrees for 60 - 70 minutes until a knife inserted comes out clean. If the top begins to brown too much before the pudding has set, place a sheet of foil over the top for the remaining cook time.
Vanilla Sauce: Add the heavy cream and the sugar to a sauce pan and heat over medium heat until the sugar dissolves. Mix the corn starch and milk together, then add to the cream mixture and continue to stir over medium heat until the sauce reaches your desired consistency. Remove from the heat and stir in the vanilla. Drizzle the sauce over the warm banana bread pudding and serve.