Preheat the oven to 350 degrees F. Grease 3 - 8 inch round pans (or one 9x13 inch pan) and line with parchment paper; set aside
In a medium bowl, combine the dry ingredients flour, baking powder, baking soda, salt, ground cinnamon, ground ginger, allspice.
In a separate bowl combine the wet ingredients; apple sauce, oil, eggs, vanilla, brown sugar, white sugar until well combined.
Add in the grated carrots, pecans, and black raisins. Gently fold them until well distributed evenly.
Pour the batter on the prepared cake pans and bake for 25-30 minutes until the toothpick inserted comes out clean.
Transfer the cakes to a cool rack and allow it to cool down for 15 minutes. Flip the cakes and remove the cake pan carefully.
To Make the Cream Cheese Frosting:
In a large bowl beat the cream cheese and butter for 5-7 minutes until they turn light and fluffy. Add in the vanilla extract and powder sugar in batches and beat them until the frosting doubles and turns white and fluffy.
To Frost:
Once the cakes have completely cooled down, slice the top of the cakes to even them out and create a flat surface using a serrated knife. Place one layer of cake on a cake stand and add about 3/4 cup of the frosting and spread out, repeat with the remaining layers. Spread the remaining frosting on top and the sides of the cake. Top with crushed or finely chopped pecans and transfer to the refrigerator or slice for serving.