Line a 9 x 13-inch baking dish with parchment paper if you want to lift the chilled dessert out easily. Combine the graham-cracker crumbs and melted butter, then press the mixture firmly into the bottom of the dish and refrigerate it while preparing the filling.

Beat the softened cream cheese and granulated sugar until smooth and creamy. Fold in about half of the thawed whipped topping, then spread the mixture evenly over the chilled crust.

Whisk both instant vanilla pudding mixes with the cold milk for about 2 minutes, or until thickened. Spread the pudding carefully over the cream-cheese layer.

Drain excess syrup from the apple pie filling and chop the apples into smaller pieces if needed. Spoon the apples evenly over the pudding layer.

Spread the remaining whipped topping over the apples. Drizzle the caramel sauce across the top and sprinkle with chopped pecans or walnuts if using.

Cover the pan and refrigerate for at least 4 hours, with overnight chilling preferred. Cut the dessert into squares with a sharp knife and serve cold.