Let bread cubes sit out and get somewhat stale.
In a large bowl, whisk eggs, milk, sugar, cinnamon, and vanilla.
Add in bread cubes and stir to coat. Place in the refrigerator for 1 hour.
Preheat the oven to 350° and spray a 9 x 13 baking dish with non-stick cooking spray.
Pour the soaked bread and all of the excess milk into the prepared baking dish, cover with aluminum foil, and bake in the preheated oven for 50-60 minutes or until a knife inserted in the center of the bread pudding comes out clean. Remove from the oven and set aside while you prepare the sauce.
In a skillet or frying pan, over medium heat, melt butter.
Add brown sugar, cinnamon, nutmeg, and cloves. Cook until sugar is completely dissolved, stirring constantly.
Add heavy cream and stir until well combined.
Stir in bananas and rum extract.
Pour sauce over baked bread pudding, Serve warm and top with a scoop of vanilla ice cream, if desired.