
Grease the pans. Preheat the oven to 325F. Grease three 8-inch pans and line the bottom of each with a circle of parchment paper.
Make the carrot cake batter. In a medium bowl, add all of the dry ingredients and whisk together. In a separate large bowl, add the eggs, butter, applesauce and vanilla extract. With a whisk or hand mixer on medium speed, blend together for 30 seconds. Add the dry ingredients into the wet ingredients and blend for another minute, until well combined. Fold in the shredded carrots and chopped pecans.
Bake the cakes. Evenly divide the cake batter between the three 8-inchpans. They'll only be about ¼ full and that's okay. Use a spatula to flatten them on top or gently tap them on the counter. Cook the cakes for 30 to 35 minutes, or until a toothpick comes out clean. Once done, let the cakes cool for 15 minutes in the pan, then remove them from the pan and continue cooling them on a cooling rack.
Make the cream cheese frosting. While the cakes are cooling, make the cream cheese frosting. Add the cream cheese, butter, powdered sugar and vanilla together to the bowl of a stand mixer and blend on medium speed, until creamy. Alternatively, you can use a large bowl with a hand mixer on medium speed.
Frost the cakes. Divide the frosting between the layers and add a thin layer of frosting to the outside edge. Use a spatula to scrape any excess off, as you would if you were crumb coating a cake. Add a sprinkle of chopped pecans on top.