Preheat the oven to 350F and grease 2 9-inch round cake pans and line with parchment paper to ensure the batter doesn't stick. Set aside.
In a large mixing bowl, sift the flour, baking soda, baking powder, and salt. Set aside.
In a large mixing bowl, add the sugars, spices, oil, vanilla, applesauce, orange zest, and eggs. Then, whisk until combined. Next, add the grated carrots and mix until combined. Be sure to scrape the sides of the mixing bowl to ensure all the batter is incorporated.
Next, pour the wet batter into the flour mixture and mix with a rubber spatula until combined. Be sure not to overmix, a few lumps are okay.
Next, evenly divide the batter in the 2 prepared pans. Bake for 30-35 minutes or until a toothpick comes out clean. Note, baking time may vary depending on your oven.
Once done, allow the cakes to cool in the pan on a wire rack until completely cooled.
Make the Frosting. In a large bowl, combine the softened cream cheese with the softened unsalted butter and beat on high until smooth and creamy. Next, mix in vanilla extract, salt, and gradually add the powdered sugar, mixing on low speed at first to prevent a sugar cloud. When the sugar is pretty much incorporated, beat the frosting for about 2 minutes on high.
Assemble Cake. Place the first layer of cake on a serving plate or cake stand, and evenly spread the top of the cake layer with frosting. Next, add the second layer and use the rest of the frosting to frost the top and sides of the cake. I like to add nuts to the top. Lately, I have been topping this cake with my candied walnuts -- SO GOOD! Refrigerate the cake for at least 30 minutes before cutting and serving.