Preheat the oven to 375°F and coat a 9x13 baking dish with nonstick spray.
In a large bowl, mix diced apples, sugar, cornstarch, cinnamon, and nutmeg until the apples are well coated.
Slice the cinnamon rolls into ¼-inch thick pieces, dust with flour, and roll each one out on a floured surface until thin.
Arrange a layer of flattened cinnamon rolls on the bottom and sides of the baking dish, pressing them together to seal.
Spread half of the apple mixture over the cinnamon roll layer and drizzle with 2-3 tablespoons of caramel sauce.
Cover with another layer of flattened cinnamon rolls.
Add the remaining apple mixture, drizzle more caramel sauce, and top with the final layer of flattened cinnamon rolls.
Cover the dish with foil and bake for 30 minutes, then remove the foil and bake for another 10-15 minutes until golden brown.
Let it cool for at least 30 minutes, then drizzle with the provided icing before serving.