To prepare the carrot cake: Begin by preheating your oven to 350°F (180°C). Generously coat two 9-inch round cake pans with nonstick cooking spray and line the bottoms with parchment paper circles for easy release. Set the pans aside. In a large bowl, combine the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt, whisking until the dry ingredients are evenly mixed. Set this bowl aside. In another large mixing bowl, whisk together the oil, eggs, packed light brown sugar, granulated sugar, applesauce, and vanilla extract until the mixture is smooth and fully blended. Stir in the grated carrots until well distributed throughout the wet mixture. Gradually pour the wet ingredients into the bowl of dry ingredients, then gently stir with a whisk or rubber spatula just until everything is combined—take care not to overmix, as this can affect the cake's texture. Evenly divide the batter between the two prepared pans and bake for 30 to 35 minutes, or until the tops are set and a toothpick inserted into the centers comes out clean. Remove the cakes from the oven and place the pans on a wire rack, allowing them to cool for 20 to 25 minutes before removing the cakes from the pans to finish cooling completely on the rack.

To make the cream cheese frosting: In the bowl of a stand mixer fitted with the paddle attachment—or using a large bowl and a hand-held electric mixer—beat the softened cream cheese until smooth. Add the softened butter and continue mixing for 30 seconds to 1 minute, until the mixture is creamy and fully combined. Add the powdered sugar and vanilla extract, then continue mixing until the frosting is completely smooth, pausing to scrape down the sides of the bowl as needed for even blending.

To assemble the cake: Once the cake layers have cooled, level the tops using a sharp knife or cake leveler if necessary. Place one cake layer on a cake stand or serving plate, then spread a little over 1/2 cup of the cream cheese frosting evenly across the top. Gently place the second cake layer on top, then use the remaining frosting to cover the top and sides of the entire cake. For a finishing touch, garnish with chopped pecans or your favorite decorative toppings, if desired.