Preheat oven to 325 degrees. Spray a muffin tin with baking spray or use paper liners.
Combine the flours, starch, baking soda, salt, cinnamon, nutmeg and ginger together in a large bowl. Set aside.
Mix the eggs, maple syrup, apple cider vinegar, and oil together in a separate bowl.
Add the carrots to the wet ingredients and mix together.
Add the wet ingredients to the flour mixture, mix together until well incorporated.
Stir in the pecans.
Fill 12 paper baking liners and place into a muffin tin.
Bake for 20 minutes, or until a toothpick comes out dry when inserted into the center of the cupcakes.
Remove from oven and allow to cool completely.
To make the Frosting:
Beat the palm shortening and maple syrup together in a small bowl until smooth and creamy.
Add the vanilla, salt, and tapioca starch and beat until well mixed.
Spread frosting over cooled cupcakes. Decorate with a whole or chopped pecan pieces if desired.
Store cupcakes in the refrigerator until ready to serve.
Notes
To make these cupcakes completely nut free, omit the pecans. Substitute raisins if desired.
I grated my carrots using the small hole on a box grater, but you could also pulverize them in your food processor if you do not want to see or feel them in your cupcakes.