Place the gingersnap cooking into a food processor and pulse until they become a fine cookie crumb.
Combine the gingersnap cookie crumbs, melted butter, and kosher salt together in a large bowl. Mix together well with your hands, squeezing to create clumps.
Press crust into a 9-inch or 10-inch springform pan and up the sides. I recommend using the back of a measuring cup or tart tamper to firmly compact the crust. This reduces the risk of it crumbling when serving.
Place the crust in the freezer while preparing the filling.
In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese (I don’t pre-soften it) until softened and smooth.
Add the dark brown sugar, granulated sugar, pumpkin puree, and pumpkin spice to the cream cheese. Continue to beat until no visible sugar granules remain.
Add the vanilla extract and kosher salt. Beat to combine.
Switch to the whisk attachment and add cream to the cream cheese mixture. Whisk together on medium-high until stiff peaks form.
Remove the crust from the freezer and scrape the cheesecake filling into the prepared crust using a rubber or silicone spatula. Spread the filling evenly and smooth it out with a small offset spatula.
Cover with plastic wrap and refrigerate for at least 2 hours. Aim to chill it for 12 hours, but overnight is best. This will allow the cleanest slices.