In a large bowl, using an electric mixer, add the cream cheese, powdered sugar, vanilla extract and the one tablespoon of milk.

Beat together until smooth.

Add half of the container of whipped topping.

Fold it gently into the cream cheese mixture.

Add it to the bottom of the prepared graham cracker crust.

Add the pudding mix to a mixing bowl.

Then add the can of pure pumpkin.

Add the pumpkin pie spice.

Finally add the milk.

Using an electric mixer, combine together until everything is smooth.

Gently spread the pumpkin pudding layer on top of the cream cheese layer.

There's no need to chill either layer yet.

Now add the remaining half of the whipped topping to the top of the pumpkin pudding layer.

Spread it around to make sure the pumpkin layer is pretty well covered.

Add chopped pecans or walnuts if you want to the top of the cheesecake.

Refrigerate the pumpkin cheesecake for at least 2 to 4 hours before serving.