Preheat oven to 300 degrees.
Place bread cubes on a baking sheet. Toast in oven until dried about 15 minutes, watching carefully so they don't brown. Let cool to room temperature, Place bread cubes in a large bowl and add vanilla waffers pieces. Set aside.
Increase oven temperature to 375 degrees, Place bananas on foil-lined baking sheet. Roast until peels are blackened, the juices ooze out and the bananas are very soft, about 45 minutes.
Meanwhile, in a bowl, whisk together whole eggs, egg yolks, and sugar. Set aside. In a saucepan over medium heat, warm the cream until it just simmers.
Scoop banana flesh into a blender. Pour any juices from the baking sheet into the blender and blend until a smooth puree forms. Gently whisk the puree into the warm cream. Slowly whisk about half the cream mixture into the egg mixture, then whisk the egg mixture into the saucepan with the remaining cream mixture. Pour the custard over the bread cubes and vanilla wafer mixture. Let stand, stirring occasionally,until ther bread cubes are very soft, about one hour. Not all of the custard will be absorbed.
Reduce the oven temperature to 350 degrees. Bring a pot of water to boil over high heat. Pour the bread mixture into an 8" square, nonstick pan and place the pan into a nonstick 9x13" pan. Fill the larger pan with boiling water to reach 1/2 way up sides of 8" pan. Cover larger pan with foil and bake for 40 minutes, Remove foil, increase oven temperature to 400 degrees and bake additional 25 minutes. Remove both pans from oven, remove 8" pan from water bath and allow to cool for 10 minutes. Serve warm or at room temperature with vanilla ice cream.