Stir the crushed gingersnap crumbs, ginger, cinnamon, melted butter, and sugar together in a bowl until everything looks like damp sand. Press the mixture firmly into the bottom and up the sides of your springform pan using the flat base of a measuring cup. The tighter you pack it, the cleaner your slices will look later. Pop the pan in the freezer while you make the filling.
In a clean bowl, beat the cold heavy cream on medium-high speed until stiff peaks form, about 4 minutes. This step is the single most important part of the whole recipe, since the whipped air is what helps the cheesecake set without any baking. Set the bowl aside in the fridge so it stays cold and firm.
Beat the softened cream cheese alone first until it's completely smooth with no lumps. Add the pumpkin puree, confectioners' sugar, and brown sugar, then mix again until fully combined. Finish with the vanilla, pumpkin pie spice, cinnamon, and salt, scraping the bowl so everything blends evenly.
Gently fold the whipped cream into the pumpkin cheesecake base using a silicone spatula, not the mixer. Work slowly in wide strokes so you don't knock the air out of the cream. This fluffy air pocket is exactly what gives the filling its light, mousse-like texture once it sets.
Pull the crust from the freezer and spoon the filling on top, spreading it evenly with an offset spatula. Cover the pan tightly with plastic wrap and refrigerate for at least 8 hours, though I always aim for 12 or more. This long chill time is what firms everything up and lets the spiced flavor really settle in.
Run a thin knife around the edge of the pan before releasing the springform sides. Wipe your knife clean between each cut for neat, bakery-style slices. Top with whipped cream or a caramel drizzle right before serving for the best presentation