1. Prepare the oven and baking dish. Preheat the oven to 350°F. Lightly grease a 9x13-inch baking dish with nonstick cooking spray. Cut each cinnamon roll into four pieces and spread them evenly in the dish.
2. Make the pumpkin mixture. In a large bowl, whisk together the pumpkin puree, eggs, milk, brown sugar, vanilla extract, pumpkin pie spice, cinnamon, salt, and melted butter until smooth.
3. Combine the ingredients. Pour the pumpkin mixture over the cinnamon roll pieces, making sure they are well coated. Gently press the pieces into the mixture so they can soak up some of the custard.
4. Bake the casserole. Bake for 30–35 minutes, or until the center is set and the cinnamon rolls are golden brown and cooked through. If the top starts browning too quickly, loosely cover the dish with foil during the last 10 minutes.
5. Add the icing and serve. Let the casserole cool for about 5 minutes. Warm the icing packets for a few seconds if needed, then drizzle the icing over the top. Serve warm with extra icing or a little maple syrup, if desired.