Heat the oven to 375°F and coat the glass or ceramic baking dish with nonstick spray. The dish should have an even coating across its bottom and sides.

Combine the diced apples, sugar, cornstarch, cinnamon, and nutmeg in a mixing bowl. Stir until the apple pieces are evenly coated and no dry starch remains at the bottom.

Slice the cinnamon rolls into 1/4-inch rounds, then flatten each round on a floured work surface with a rolling pin or flour-dusted hands. The pieces will feel sticky, but they should become thin enough to form pastry layers.

Fit a layer of flattened dough across the bottom and up the sides of the prepared dish, pressing adjoining pieces together. Look for a joined surface without large gaps beneath the fruit.

Spread half the apple mixture over the dough, drizzle with 2 to 3 tablespoons of caramel sauce, and add another layer of flattened dough. The apples should reach across the dish without piling heavily in the center.

Add the remaining apples, drizzle with more caramel sauce, and cover with the remaining flattened dough. Press the top pieces together so the fruit sits beneath a mostly continuous pastry layer.

Cover the dish with aluminum foil and bake for 30 minutes; remove the foil and bake for another 10 to 15 minutes. The top should turn golden brown, with bubbling filling visible near the edges.

Let the dish cool for at least 30 minutes, then drizzle with the icing from the cinnamon roll cans and slice. The filling will settle as it cools, making the layers easier to serve.