Preheat oven to 350°.
Beat the honey and olive oil with an electric mixer until smooth and creamy. Add eggs one at a time and beat well after each addition. Continue to beat until everything is blended well.
In a separate bowl, combine arrowroot flour, brown rice flour, xanthan gum, baking soda and spices and mix with a wire whisk.
Add flour mixture to creamed mixture and mix until combined. Fold in carrots.
To make a cake, pour batter into a lightly oiled 13x9 inch pan.
Bake for about 30 minutes or until toothpick inserted in center of cake comes out clean.
To make cupcakes, line a cupcake pan with paper liners and fill each cup about ¾ full. Bake for 20-25 minutes or until toothpick inserted in center comes out clean.
Frost with your favorite frosting or enjoy plain...delicious either way.