Make the crust: In a mixing bowl, combine the gingersnap crumbs, sugar, ground ginger, cinnamon, and melted butter. Stir until all the crumbs are moistened. Press the mixture firmly into a 9- or 10-inch springform pan, using the bottom of a measuring cup to press down evenly and compact the crust along the bottom and slightly up the sides. Place the pan in the freezer to chill for 10–20 minutes while you prepare the filling.
Make the filling: In a separate bowl, use a hand mixer or stand mixer fitted with a whisk attachment to whip the cold heavy cream on medium-high speed until stiff peaks form, about 4 minutes. Set the whipped cream aside.
In another large mixing bowl, beat the softened cream cheese on medium speed until completely smooth and creamy, scraping down the sides and bottom of the bowl as needed. Add the pumpkin puree, confectioners’ sugar, and brown sugar, and continue to beat on medium-high speed until fully blended and creamy. Scrape down the bowl again to ensure all ingredients are well incorporated. Add the vanilla extract, pumpkin pie spice, cinnamon, and salt, then beat until everything is smooth, creamy, and no lumps of cream cheese remain.
Using a mixer on low speed or a silicone spatula, gently fold the whipped cream into the cream cheese mixture. Take care to incorporate the whipped cream slowly, preserving its airy texture.
Assemble the cheesecake: Retrieve the prepared crust from the freezer. Spread the pumpkin cheesecake filling over the crust, using an offset spatula to smooth the top evenly.
Cover the pan tightly with plastic wrap or aluminum foil, then refrigerate the cheesecake for at least 8 hours, or ideally overnight for 12 hours, to achieve the best set. Avoid freezing as it may impact the creamy texture.
When ready to serve, run a knife along the edges of the springform pan to loosen the cheesecake. Release and remove the rim, then slice the cheesecake with a sharp, clean knife, wiping the blade between each cut for tidy slices.
Top with whipped cream, salted caramel, or your preferred garnish. Store any leftovers in the refrigerator for up to 5 days.