Preheat oven to 350ºF. Spray a 9x13 baking dish with cooking spray. Set aside.
In a large bowl add the applesauce, eggs, brownsugar, whitesugar, milk and groundcinnamon. Whisk to combine.
Add the breadcubes and toss lightly to coat. Allow to sit for a few minutes. Add to prepared baking dish and sprinkle the remaining 2 tablespoons of brownsugar over the top.
Bake uncovered for 50-55 minutes, or until the center is set and the pudding has puffed. Remove from the oven and cool for a few minutes.
For the Vanilla Icing
To a small bowl add the powderedsugar, vanilla, and milk and stir to combine. Drizzle over the warm bread pudding and serve immediately.