Preheat the oven to 350º F.
In a large bowl, add all of the dry ingredients and whisk to blend.
Grate carrots with a grater, or a food processor.
Add wet ingredients to a bowl. Mix well then add carrots and mix to blend.
Pour the wet ingredients into the dry ingredients and mix.
Add paper cupcake liners to a muffin tin and fill each ¾ with the cake batter.
Bake for 20-25 minutes.
Remove from the oven and take cupcakes out of the muffin tin. Put them on a cooling rack and allow them to cool all of the way.
In a mixer, add all frosting ingredients and mix until fluffy.
Put the frosting into a frosting bag and squeeze the frosting out onto each cupcake.
*Optional: sprinkle coconut on top of each cupcake.