Preheat the oven to 350°F. Grease two 9-inch round cake pans and line the bottoms with parchment paper.

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg.

In a large bowl, whisk together the brown sugar, granulated sugar, and vegetable oil. Add the eggs and whisk until well combined, then whisk in the applesauce and vanilla.

Add the dry ingredients to the wet ingredients and mix until just combined. Fold in the carrots and pecans.

Divide the batter evenly between the prepared pans. Bake for 30 to 35 minutes, or until the tops spring back to the touch and a toothpick inserted comes out clean. Let cool in the pans for 10 minutes. Run a knife around the edge of each cake, then invert onto a large plate or baking sheet. Transfer to a cooling rack and allow to cool completely.

Optional step: When the cakes are completely cool, use a large serrated knife to slice off the domed part of one of the cakes to create a flat top. Use this cake as the bottom layer in a layer cake.

Frost the flat surface with cream cheese frosting, then place the second cake layer on top. Frost the top and sides of the cake, if desired, with the remaining frosting. Top with more pecans, slice, and serve. (Alternatively, enjoy this recipe as two single-layer cakes.)