Line cupcake tins with liners. (Or grease and lightly flour two round, 9 x 1 1/2 inch baking pans).
Shred carrots with a medium sized grater. Set aside.
Preheat oven to 325° F
In a large bowl, combine flour, sugar, xanthan gum, baking powder, baking soda, salt and cinnamon. Stir well to combine.
Add to the dry mixture, the shredded carrots, oil, flax and water (or eggs). Mix with an electric mixture until thoroughly blended.
Spoon into cupcake tins about 2/3 full (or into round pans).
Bake at 325° F for;
15-20 minutes for mini cupcakes
20-25 minutes for regular cupcakes
30-40 minutes for round cakes
You know they are done when the cake springs back with a light touch of the finger.
Remove from oven and allow to cool to room temperature before frosting.
Store in refrigerator, serve at room temperature.