Put oven rack in the middle position. Preheat oven to 350°F/175°C.
In the same food processor bowl (no need to even wash it), add the pumpkin, sugars, vegan creamer, vanilla, liqueur (if using), cornstarch, spices, and salt. Pulse in quick bursts until the ingredients are combined. Add vegan cream cheese and pulse again until creamy and smooth. Be sure to use a spatula to push down any ingredients along the sides of the food processor bowl.
Pour filling into the crust, smoothing the top with a spatula.
Baking without a water bath: Place the pan in a shallow baking pan. Bake until the center is just set, 50 to 60 minutes. Turn the heat off and leave the cheesecake in the oven for another hour.
Baking with a water bath: Wrap the bottom and sides of the springform pan with foil. Place the pan in a larger roasting pan. Place the roasting pan in the oven and pour about 2 cups of water into the roasting pan. Close the oven door and bake the cheesecake for 55 to 60 minutes. The center of the cheesecake should be slightly jiggly. Turn the heat off and leave the cheesecake in the oven for another hour.
Cool cheesecake completely in pan on a rack, about 3 hours. Then cover and refrigerate for 3 to 4 hours (or overnight).
To serve, remove sides of the pan and bring to room temperature. Serve with vegan caramel sauce and vegan whipped cream. Baked cheesecake can be chilled, covered, up to 5 days (if it lasts that long!) in the fridge. It can also be frozen. I prefer to cut it into individual slices. These will keep in the freezer for up to 2 months.