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Preheat the oven to 350 degrees F. Line two 9-inch cake rounds with parchment paper.
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In a measuring cup, combine the almond milk and vinegar. Let sit for a few minutes.
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In a large mixing bowl, combine the brown sugar, vegetable oil, applesauce, eggs, and vanilla. Whisk until well combined.
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In another mixing bowl, combine the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, cloves, and allspice. Stir until well combined.
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Add the dry ingredients to the wet ingredients. Pour in the almond milk and vinegar mixture. Stir until combined.
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Divide the batter evenly between the two 9-inch round pans. Bake at 350 degrees F for 25-30 minutes, or until a toothpick pulls out clean from the center.
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Let the cake cool for 10 minutes in the pan, then remove to a cooling rack to finish cooling completely.
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When the cake is cool, prepare the frosting: Combine the dairy-free cream cheese, dairy-free butter, powdered sugar, and vanilla in the bowl of a stand mixer (or use a mixing bowl with a hand mixer). Use the whisk attachment on the mixer to combine the ingredients, starting on slow speed until incorporated then mixing on high speed until the frosting is light and fluffy.
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Place one cake on a cake stand, and frost the top. Place the other cake on top and finish frosting the top of that cake, and sides if desired. Enjoy!