In a medium bowl, combine the crushed graham crackers and melted butter, mixing until well-blended. Press into a 9x13-inch dish and refrigerate for 15 minutes.

In a large mixing bowl, whisk together the instant vanilla pudding mix and milk for about 2 minutes until thickened. Gently fold in the pumpkin puree and pumpkin pie spice until fully incorporated.

Pour the pumpkin cheesecake filling over the chilled crust and spread evenly with a spatula.

In a separate bowl, mix any remaining pumpkin mixture from the filling, then spread it over the cheesecake layer.

Spread the thawed whipped topping evenly over the pumpkin layer, and dust with pumpkin pie spice if desired.

Cover with plastic wrap and refrigerate for at least 4 hours, preferably overnight, for the best flavor and setting.