Heat the oven to 325F. Stir the graham cracker crumbs, cane sugar, cinnamon, and salt together in a bowl, then pour in the melted vegan butter and mix until the crumbs look like wet sand and hold together when you squeeze a handful. Press the mixture firmly into the bottom and about an inch up the sides of a 9-inch springform pan, using the flat bottom of a glass to even it out. Bake for 10 minutes, then set the crust aside to cool while you make the filling.

Drain the silken tofu and pat it dry with a clean towel. Add the tofu, pumpkin puree, cane sugar, brown sugar, melted coconut oil, lemon juice, apple cider vinegar, vanilla, pumpkin pie spice, and salt to a blender and blend on high for a full minute, until the mixture is completely smooth with no visible curds. Scrape down the sides, add the cornstarch, and blend for another 15 seconds just to combine.

Pour the filling over the cooled crust and smooth the top with a spatula. Tap the pan on the counter a couple of times to knock out large air bubbles.

Wrap the bottom and sides of the springform pan in a layer of heavy foil so no water can seep in. Set the pan inside a larger roasting pan, put the whole thing in the oven, and carefully pour boiling water into the roasting pan until it comes about an inch up the side of the springform.

Bake for 55 to 65 minutes, until the outer two inches of the filling look set and the center still wobbles gently when you nudge the pan. Turn the oven off, crack the door open a few inches, and leave the cheesecake inside for 1 hour to cool slowly.

Take the pan out of the water bath and let the cheesecake come to room temperature on the counter, about 1 hour. Cover it and chill in the fridge for at least 8 hours, or overnight, until fully firm.

Run a thin knife around the inside of the pan to loosen the cheesecake, release the springform ring, and slice with a knife wiped clean between cuts. Serve cold with vegan whipped cream.