In a large mixing bowl, stir together 1 can (15 ounces) pure pumpkin puree, 1 box (3.4 ounces) instant vanilla pudding mix, ¼ cup milk, 1 teaspoon ground cinnamon, and 1 teaspoon pumpkin pie spice until smooth and well combined.
Fold in 1 container (8 ounces) whipped topping until no streaks remain.
Spoon the pumpkin mixture into 1 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.