Preheat the oven to 350°F and lightly grease a medium baking dish or large loaf pan.
In a large bowl, whisk together all bread pudding ingredients except the cinnamon rolls until smooth.
Fold in the cinnamon roll pieces until fully coated and evenly distributed.
Pour the mixture into the prepared pan and gently press down so the rolls soak up the custard.
Bake for 40 to 45 minutes, until set in the center and lightly golden on top.
While baking, mix all icing ingredients until smooth and creamy.
Spread the icing over the bread pudding while warm.
Slice, serve, and accept that this is now the superior use of cinnamon rolls.