In a large bowl, use an electric mixer to beat heavy cream until it begins to thicken. Gradually mix in ½ cup powdered sugar. Beat until soft peaks form. Scrape whipped cream into a separate bowl and set aside.
In the same bowl used to whip the cream, beat the cream cheese until smooth. Slowly blend in remaining 1 cup powdered sugar and beat until smooth. Blend in pumpkin, spices, and vanilla and beat until well combined. Gently fold whipped cream into pumpkin mixture and set aside.
Dollop a bit of the pumpkin mixture into the bottom of a 9- by 13-inch baking dish and spread into a thin layer. Cover with a layer of gingersnaps. Spoon about ⅓ of the remaining pumpkin mixture over the gingersnaps and spread into an even layer. Repeat gingersnap layer and pumpkin layer two more times. Sprinkle with a few crushed gingersnaps, if desired. Cover and refrigerate for 8 hours or overnight.
