Preheat the oven to 375°F (190°C). Generously grease a 9x13 inch baking dish with butter or non-stick cooking spray.

Open the cans of cinnamon rolls and immediately set both containers of icing aside. Place the rolls on a cutting board and cut each roll into four quarters (you should have 32 pieces total). Place all the cut pieces into a very large mixing bowl.

Prepare the Flavor Mixture: In a small bowl, melt the 4 tablespoons of butter. Whisk in the ½ cup of packed brown sugar and the 1 teaspoon of ground cinnamon until combined. Pour this mixture over the cut cinnamon roll pieces and toss gently using a rubber spatula until the rolls are evenly coated.

Create the Custard: In a separate medium bowl, whisk together the 4 large eggs, ½ cup of whole milk (or half-and-half), 1 teaspoon of vanilla extract, and a pinch of salt until fully blended and slightly frothy.

Combine and Transfer: Pour the egg and milk custard mixture over the sugar-coated cinnamon roll pieces. Fold the ingredients together gently once more to ensure all the roll pieces are coated in the liquid. Transfer the entire mixture into the prepared 9x13 inch baking dish, spreading the pieces out evenly.

Bake for 25 to 30 minutes, or until the edges are golden brown and bubbling, and the custard is fully set in the center (it should not look liquid when the pan is jiggled).

Remove the casserole from the oven and let it cool for about 5 minutes. Open the reserved icing containers. If the icing is stiff, warm it for 5-10 seconds in the microwave or whisk in about ½ teaspoon of milk to loosen it. Drizzle the entire amount of icing evenly over the warm casserole.

Serve the Cinnamon Roll Casserole immediately while warm.