Preheat your oven to 350°F (175°C). Grease and flour your 9-inch round cake pans.
In a large mixing bowl, whisk together the all-purpose flour, ground cinnamon, ginger, nutmeg, baking soda, baking powder, and salt. Set aside.
In another bowl, combine the vegetable oil, light brown sugar, and granulated sugar. Beat in the eggs one at a time, followed by the applesauce and vanilla extract until well blended.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Be careful not to overmix.
Fold in the grated carrots and chopped pecans, ensuring they are evenly distributed throughout the batter.
Divide the batter evenly between the prepared cake pans. Bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean. Let the cakes cool in the pans for 10 minutes before transferring them to a cooling rack.
In a large bowl, beat together the softened cream cheese, unsalted butter, and vanilla extract until smooth. Gradually add the powdered sugar and continue to beat until light and fluffy.
Once the cake layers are completely cool, place one layer on a serving plate. Spread a generous amount of cream cheese frosting on top, then place the second layer on top. Frost the top and sides of the cake with the remaining frosting.
