In the bowl of your stand mixer, whip the whipping cream on high speed until soft peaks form. Use a powdered stabilizer, if desired (I like the one from Dr. Oetker called 'Whip It').
When the whipping cream has reached the soft peaks stage, drizzle in the sweetened condensed milk slowly as the cream continues to whip. Continue adding in a slow, steady stream until it's all been added.
Add the pumpkin pie spice and also the pumpkin by the small spoonful as well, after the sweetened condensed milk. Be sure not to over-whip the cream so it separates, so act quickly (have all the ingredients ready to go before you start).
Line the bottom of a 9-inch by 13-inch baking dish (I use glass or pyrex) with one layer of gingersnap cookies.
Top the cookies with one third of the pumpkin cream mixture, smoothing out the top. Add another layer of gingersnap cookies, the 2nd third of the pumpkin cream mixture, and repeat with one more later of cookies, and the remainder of the cream mixture.
Top with more crushed gingersnap cookies.
Refrigerate uncovered (to prevent condensation) for about 12 hours or overnight, before slicing and serving.