Preheat your oven to 350 Fahrenheit or 176 Celcius.
Make the batter: Get out a large mixing bowl and whisk together the flour, baking soda, salt, cinnamon, ginger, nutmeg, and cardamom. In another large mixing bowl whisk the brown & granulated sugar, eggs, oil, apple sauce, and vanilla extract together until they are thoroughly incorporated. Then pour the wet ingredients into the bowl of dry ingredients and use a spatula, or wooden spoon to combine the two. Finally, toss in the grated carrots along with the chopped nuts, and fold both ingredients into the batter.
Distribute the batter between two 9-inch cake pans that have been greased with either butter or some type of spray, like PAM.
Bake the cakes: Place the two cakes into the center rack of your oven and let them bake for 30 to 35 minutes. You will know that the cakes are done when they become dark brown, and it passes the toothpick test.
Let the cakes cool: Take the fully baked cakes out of the oven and let them cool in their pans on a wire rack for 20 minutes. Then remove the cakes from their pans and let them finish cooling on wire racks for 40 minutes to an hour.
Make the frosting: After the cakes have completely cooled it’s time to make the frosting. Start by beating the cream cheese and butter together in either a stand mixer or mixing bowl. Next, add in the vanilla extract and beat it into the cream cheese/butter mixture. Then slowly add in the powdered sugar and continue to beat until everything is incorporated.
Assemble and frost the cake: Start by laying one cake down on a plater or cake stand. Then spread a light layer of the cream cheese frosting over the top of this cake. Place the second cake on top of this, and use a spatula to spread a layer of the cheesecake on both the sides and the top. At this point the cake is done, however, you can also add in some decorations or crushed nuts.
Let the cake chill in a fridge for an hour to let the frosting set up. Then you are free to slice it up and enjoy.