Preheat oven to 350 degrees Fahrenheit (175 degrees Celsius).
Butter two 9-inch round cake pans, line with parchment paper, and butter parchment paper. Dust parchment paper with flour and shake out excess. If available, line pans with water-soaked cake strips.
In a mixing bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger.
In a large mixing bowl using an electric mixer, blend together vegetable oil, applesauce, eggs, granulated sugar, brown sugar, and vanilla.
Add dry ingredients to the wet mixture and mix until combined. Mix in grated carrots just until evenly distributed. Divide mixture evenly into the prepared cake pans.
Bake in the preheated oven for 33 - 38 minutes or until a toothpick inserted into the center comes out clean.
Remove from oven and allow to cool for 10 minutes in the cake pans. Then, run a knife around the edges of the cakes and invert them onto a wire rack to cool completely.
Frost cakes with cream cheese frosting and finish with chopped pecans if desired. Store cake in an airtight container in the refrigerator.