Preheat your oven to 325°F. Line a 9x13 inch cake pan with parchment paper, making sure the sides are covered too.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and spices. Set this aside for now.
In a large bowl, whisk the sugars and oil until combined.
Add the eggs, vanilla, sour cream, and applesauce one at a time, mixing well after each addition. Don’t forget to scrape down the sides of the bowl as needed.
Sift the flour mixture into the wet ingredients and gently fold until only a few dry streaks remain. Then, fold in the shredded carrots.
Pour the batter into your prepared pan and bake for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool completely before adding any frosting. Once it has cooled, you can easily lift it out of the pan using the edges of the parchment paper.