Preheat oven to 350℉ (177℃). Line three 8-inch pans with parchment paper circles.
In a large bowl, beat the granulated sugar, brown sugar, applesauce, oil, eggs, and vanilla on medium-high speed until combined. Stir in the shredded carrots.
1 1/4 cups oil, 1/4 cup applesauce, 1 cup (200g) brown sugar, 1 cup (200g) granulated sugar, 4 large eggs, 2 teaspoons pure vanilla extract, 3 cups finely shredded carrots
Add the flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, and cloves. You can always whisk these together in a separate bowl first, which is what a lot of bakers do, but I feel like if you sprinkle the spices over the flour instead of dumping them, you can save yourself a bowl and a step and they will mix in just fine without any clumps of cinnamon or cloves.
2 1/2 cups (353g) all-purpose flour, 2 teaspoons baking powder, 1 teaspoon baking soda, 1 teaspoon salt, 1 teaspoon ground cinnamon, 1/2 teaspoon ground nutmeg, 1/2 teaspoon ground ginger, 1/4 teaspoon ground cloves
Divide the batter evenly between the prepared cake pans.
Bake for 20-25 minutes until a toothpick inserted into the center of the cake comes out clean with just a few crumbs on it. Cool for a few minutes in the pans before turning them out onto a wire cooling rack to cool completely.