In a large mixing bowl, whisk together the instant pudding mix, cold milk, pumpkin puree, and pumpkin pie spice until the mixture is completely smooth and lump-free. Whisk for about 2 minutes, then place the bowl in the refrigerator for 10 minutes to allow the pudding to thicken slightly.
Once the pudding has thickened, gently fold in the whipped topping using a spatula. Mix just until combined the goal is to keep the mixture light and airy, so avoid overmixing.
Spoon or pipe the pumpkin pudding mixture into small clear dessert cups or jars for a pretty layered look. If desired, add a layer of crushed cookies or granola between the pudding layers for extra texture and flavor.
Cover the cups with plastic wrap and refrigerate for at least 30 minutes. This helps the flavors meld together and gives the pudding a firmer, creamier consistency.
Just before serving, top each cup with a swirl of whipped cream, a light sprinkle of cinnamon, and a small cookie or handful of granola for garnish. Serve chilled and enjoy!