The night before, cut the bread into 1-inch cubes and lay it on a sheet tray. Place it in a cold oven overnight to dry out. (see note)
Add the milk, Fireball, sugar, brown sugar, and cinnamon to a small saucepan over medium heat. Stir constantly until the sugars are melted, about 5 minutes.
Add the butter to the pot and stir until melted. Remove from the heat and stir in the vanilla. Set aside.
Place the dried bread cubes into a large bowl. Pour the milk mixture over the bread and stir to combine. Set aside to rest at room temperature for 30 minutes so the liquid can soak into the bread.
Preheat your oven to 350 degrees F. Spray the inside of a 9-inch x 13-inch baking dish with non-stick cooking spray. Set aside.
Dice the peeled apples. Put the apples and beaten eggs into the bowl with the bread pudding mixture. Fold everything together until well combined. Pour the bread pudding mixture into the prepared baking dish, spreading it into an even layer.
Bake for 50-55 minutes until golden brown on the top and the edges begin to pull away from the sides. A knife inserted into the center should come out clean.
Remove from the oven and place on a wire rack to cool for 15 minutes.
While the bread pudding is cooling, make the sauce. Add the sugar, heavy cream, and butter to a small saucepan. Stir constantly over medium heat until the butter is melted and the sugar has dissolved, about 5 minutes. Remove from the heat and stir in the Fireball.
Slice the bread pudding into 15 squares. Serve the warm bread pudding with some of the sauce spooned over top.
Notes
Nutritional information includes 1 slice of bread pudding with 2 tablespoons of sauce.
You can quick-dry the bread cubes by cooking them on a baking sheet in a 250-degree F oven for 20-30 minutes, flipping them every 10 minutes until crisp.