Preheat ocen to 350 then line 2 baking sheets with silicone baking mats (preferred) or parchment paper
In a medium bowl whisk together the flour, xanthan gum, baking powder, baking soda, cinnamon, ginger, all spice, cloves and salt until combined. Set it aside.
Using an electric mixer cream together the butter, brown sugar, and granulated sugar together until smooth and creamy.
Add the shredded carrots, vanilla and egg and mix until combined and smooth.
Add in the flour mixture and mix until a smooth thick batter is formed.
Using an ice cream scoop, scoop 10 equal sized cookie dough balls and place them on the prepared baking sheets.
Bake them for 15-17 minutes. Let them cool on the baking sheet for 20 minutes then gently transfer them to a cooking rack.
Prepare the frosting