In the bowl of a stand mixer fitted with the whisk attachment, combine the heavy whipping cream, confectioners’ sugar and vanilla extract. Whisk it on high speed until stiff peaks form.
Transfer the whipped cream to a bowl then wipe out the mixing bowl.
Attach the beater blade to the stand mixer.
To the clean mixing bowl, add the cream cheese and beat until smooth then beat in the pumpkin puré, vanilla pudding, milk and pumpkin pie spice until combined, scraping down the sides as needed.
Fold in half of the prepared whipped cream then refrigerate the mix for a minimum of 30 minutes and up to overnight.
When ready to serve, layer the crushed gingersnap cookies and pumpkin cheesecake filling. Top with the remaining 1/2 of the prepared whipped cream and serve.