Preheat your oven to 350°F (175°C). Prepare two 9-inch round cake pans by buttering them, lining with buttery parchment paper, sprinkling some flour, and shaking out the excess. Use cake strips for even baking if available.

In a mixing bowl, combine the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger. Whisk these dry ingredients together for even distribution.

In a large mixing bowl, blend the vegetable oil, applesauce, eggs, granulated sugar, brown sugar, and vanilla extract using an electric mixer on medium speed until smooth.

Slowly incorporate the dry ingredients into the wet mixture. Mix just enough to combine. Gently fold in the grated carrots.

Pour the batter evenly into the prepared cake pans. Smooth out the tops with a spatula.

Bake for approximately 35 to 40 minutes, or until a toothpick inserted in the center comes out clean.

Let the cakes cool in the pans for 10 minutes, then carefully invert onto a wire rack to cool completely.

Once cooled, frost them with cream cheese frosting and sprinkle with chopped pecans if desired.