Preheat your oven to 350°F. Grease two 9-inch round cake pans with non-stick spray and line the bottoms with parchment paper circles. Set aside.

In a large bowl, whisk together the flour, cinnamon, baking powder, baking soda, ginger, nutmeg, and salt until fully blended. Set aside.

In another large bowl, whisk together the oil, eggs, brown sugar, granulated sugar, applesauce, and vanilla extract until smooth. Add the grated carrots to the wet mixture and stir until well incorporated.

Combine the wet and dry ingredients, mixing gently with a whisk or rubber spatula until just combined. Avoid over-mixing the batter.

Divide the cake batter evenly between the prepared pans. Bake for 30 to 35 minutes, or until the tops are set and a toothpick inserted into the center comes out clean.

Remove the cakes from the oven and place on a wire rack to cool in the pans for 20 to 25 minutes. Once slightly cooled, remove the cakes from the pans and allow them to cool completely on the wire rack.

In a stand mixer with a paddle attachment, or in a large bowl with a hand mixer, beat the cream cheese until smooth. Add the butter and continue mixing for 30 seconds to 1 minute until well combined and creamy.

Gradually add the powdered sugar and vanilla extract, mixing until fully incorporated and smooth, scraping down the sides of the bowl as necessary.

To assemble the cake: Level the tops of the cooled cakes with a knife or cake leveler. Place one cake layer on a serving plate, spread a little over 1/2 cup of frosting on top, and smooth it out evenly. Place the second cake layer on top and use the remaining frosting to cover the top and sides of the cake. Garnish with pecans or other desired toppings.