Preheat your oven to 350 degrees and line a muffin tin with 6 muffin liners. Set aside.
In a medium mixing bowl,stir together the sifted coconut flour, baking soda, baking powder, cinnamon, nutmeg and salt until well combined. Set aside.
In a large bowl, using an electric hand mixer, beat together the eggs, coconut oil, vanilla extract and brown sugar until light and fluffy.
Stir in the coconut flour mixture, and then beat it to make sure that the lumps are completely gone.
Stir in the grated carrots until all the carrots are mixed in and coated in the batter.
Pour the batter into the prepared muffin tins and let stand 10 minutes before baking.
Bake for 20-22 minutes or until the top is golden and a toothpick inserted in the center comes out clean.
Let cool completely before assembling.
To make the green coconut:
Mix the water and desired amount of green food coloring in a small baggie.
Add in the coconut and swirl around until all the coconut is covered.
Lay out on a paper towel to dry and set aside. ***
To make the frosting:
In a large bowl, beat together the softened cream cheese and butter until light and fluffy (about 5 mins.)
Beat in the vanilla until well combined.
Turn the mixer down to low and gradually beat in the powdered sugar.
Turn the speed back up and beat for an additional 2-3 minutes, until light and fluffy.
Using a small spoon, scoop a little circle out of the center of each mini carrot cake.
Spoon the icing into a parchment bag and fill the hole with frosting, swirling it just over the top of the cake as well.
Sprinkle with colored coconut and Mini eggs.
* I also had success using coconut sugar instead of brown sugar, although most people slightly preferred the taste of the brown sugar version. Note that coconut sugar makes baked goods go VERY dark brown, and it is wise to cover the top of the cake with parchment paper for the last 10 minutes of baking.br] **Cream cheese icing recipe from [About.com***You can also speed up the drying by placing the coconut on a small baking sheet into the oven at 450 degrees for 2-3 minutes.