Preheat the oven to 350 degrees F. Wrap aluminum foil around the bottom and halfway up the sides of a 9-inch springform pan to prevent any leaking.
Combine the cream cheese, agave, soy milk, pumpkin, tofu, arrowroot, agar, cinnamon, and nutmeg in a large mixing bowl and stir together. Transfer to a blender and blend until smooth and ingredients are fully integrated. This may have to be done in batches. Pour the mixture into the prepared springform pan.
Put the cheesecake in a large baking pan and fill the pan halfway with hot water. Bake for about 2 hours, until lightly browned. Remove, let cool, cover, and refrigerate. The cheesecake can be made up to 2 days ahead of time.
To make the cider reduction, combine the cider, sugar, and nutmeg in a pot and bring to a simmer over medium heat. Simmer, stirring occasionally, until the mixture is reduced by half and is syrupy, 1 to 1 1/2 hours. The reduction can be made and refrigerated up to 2 hours ahead of time. Bring to room temperature before serving.
To make the frosting, mix together the confectioners' sugar and buttery spread in a large bowl. Set aside. Combine the coconut meat and vanilla extract in a blender and blend for 2 minutes. Transfer to a stand mixer or to a bowl and use a hand mixer. Add the confectioners' sugar mixture and cream cheese and mix thoroughly until a smooth frosting is formed.
To serve, remove the foil from the pan. Run a knife around the outer edge of the cheesecake and release the springform pan clamp. Put the cake on a plate or cake stand. Pipe frosting on the pie as desired. Drizzle the reduction over the cheesecake. Cut into wedges and serve.
"Vegan Holiday Cooking from Candle Cafe" by Joy Pierson, Angel Ramos and Jorge Pineda © 2014 by Candle Family Foods, LLC. Published in the United States by Ten Speed Press. Provided courtesy of Candle Cafe. All rights reserved.
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