In a large mixing bowl, stir together pure pumpkin puree, instant vanilla pudding mix, milk, ground cinnamon, and pumpkin pie spice until smooth and well combined.
Fold in whipped topping until no streaks remain.
Spoon the pumpkin mixture into prepared 9-inch graham cracker crust and spread it into an even layer with a spatula.
Cover and refrigerate for at least 4 hours, or overnight, until the pie is firm and fully set.
Slice into 8 pieces and serve topped with whipped cream, if desired.