Preheat the Oven and Prepare Pans: Preheat your oven to 350°F (175°C). Grease and flour two 9-inch cake pans.
Mix Dry Ingredients: In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger.
Combine Wet Ingredients: In another bowl, mix the sugar, applesauce, vegetable oil, and almond milk until well combined.
Combine Wet and Dry Mixtures: Add the wet mixture to the dry mixture and stir until just combined. Fold in the grated carrots, walnuts, and raisins.
Bake the Cake: Pour the batter evenly into the prepared pans. Bake for about 30 minutes, or until a toothpick inserted into the center comes out clean.
Make the Frosting: While the cake cools, beat together the vegan cream cheese, vegan butter, powdered sugar, and vanilla extract until smooth and creamy.
Assemble the Cake: Once the cakes are completely cool, spread frosting on the top of one cake layer, place the second layer on top, and frost the top and sides of the cake.
Decorate: Optionally, sprinkle some chopped walnuts or cinnamon on top for decoration.