Preheat oven to 350F. Prepare two muffin tins (with 12 wells each) with cupcake liners. Set aside.
In a large bowl, beat together granulated sugar and eggs for 2 minutes, until thoroughly combined and light in color.
Add in the oil, applesauce, vanilla and apple cider vinegar. Mix until combined.
In a medium bowl, combine gluten free flour blend, baking powder, baking soda, cinnamon, ginger, nutmeg, cloves and salt. Whisk to combine.
Gradually add the dry ingredients to the wet ingredients, stirring in between, until no steaks of white remain.
Stir in the shredded carrots.
Pour the batter into the prepared muffin cups, filling each 3/4 of the way full.
Bake at 350F for 18-22 minutes, until a toothpick inserted into the center of the cupcake comes out clean. Remove from the oven and let cool completely on a wire rack.