In a large bowl, combine the pumpkin puree, heavy cream, powdered sugar, vanilla extract, and pumpkin pie spice. Mix until smooth and well combined.
In a separate bowl, prepare the vanilla pudding mix according to package instructions using 2 cups of milk. Stir until thickened.
In a trifle dish or large glass bowl, layer half of the crushed ginger snap cookies at the bottom.
Spread half of the pumpkin mixture over the cookies, followed by half of the vanilla pudding.
Repeat the layers with the remaining ingredients.
Top the final layer with whipped topping and sprinkle with any remaining crushed ginger snaps for garnish.
Chill the trifle in the refrigerator for at least 2 hours before serving to allow the flavors to meld.