Prep the pan. Line the bottom of a 9-inch springform pan with parchment and lightly grease the sides.
This makes unmolding easier and keeps the crust crisp.
Make the crust. Pulse graham crackers or gingersnaps in a food processor until fine. Add granulated sugar and melted butter, and pulse until the crumbs look like wet sand. Press the mixture firmly into the pan, going slightly up the sides.
Chill for 15 minutes to set.
Bloom the gelatin (optional but helpful). Sprinkle gelatin over 2 tablespoons cold water in a small bowl. Let it stand 5 minutes. Warm in the microwave for 10–15 seconds until just dissolved.
Cool slightly while you prepare the filling.
Whip the cream. In a cold bowl, beat heavy cream to stiff peaks. Set aside in the fridge. Cold cream whips faster and holds its shape better.
Beat the cream cheese. In a large bowl, beat softened cream cheese until smooth and fluffy, about 2 minutes.
Scrape the bowl well to remove any lumps.
Flavor the base. Add powdered sugar, brown sugar, vanilla, cinnamon, pumpkin pie spice, and salt. Beat until smooth and creamy. Taste and adjust sweetness or spice if you like.
Add pumpkin. Mix in the pumpkin puree until fully combined.
The mixture should be silky and slightly thick. If using gelatin, whisk in the dissolved gelatin now, mixing thoroughly.
Fold in the cream. Gently fold the whipped cream into the pumpkin mixture in two additions. Use a spatula and light motions to keep the volume.
Stop as soon as no white streaks remain.
Fill and smooth. Pour the filling over the chilled crust. Smooth the top with an offset spatula. Tap the pan lightly on the counter to remove air bubbles.
Chill to set. Cover and refrigerate at least 6 hours, preferably overnight.
The longer chill helps the cheesecake slice cleanly and hold its shape.
Unmold and garnish. Run a thin knife around the edge before releasing the springform. Top with swirls of whipped cream, a sprinkle of cinnamon, or chopped pecans if you like.
Slice smart. Use a hot, dry knife for neat slices, wiping between cuts. Serve chilled.