Preheat oven to 350F. Grease and line two 8-inch round cake pans. Set aside.
In a medium bowl, combine the gluten-free flour blend, baking powder, baking soda, ground cinnamon, ground ginger, nutmeg, cloves, and salt. Whisk to combine.
In a large bowl, add the granulated sugar, brown sugar, and eggs. Beat together for 2 minutes, until thoroughly combined and light in color.
Add in the oil, applesauce, vanilla and apple cider vinegar. Mix until combined.
Gradually add the dry ingredients to the wet ingredients, stirring in between, until no streaks of white remain.
Stir in the shredded carrots.
Pour the batter into the prepared cake pans, filling each equally.
Bake at 350F for 33-37 minutes, until a toothpick inserted into the center of the cake comes out clean. Remove from the oven and let cool completely on a wire rack.