Preheat your oven to 350 degrees Fahrenheit and line a muffin tin with 6 muffin liners.
In a medium mixing bowl, stir together the sifted coconut flour, baking soda, baking powder, cinnamon, nutmeg, and salt until well combined.
In a large bowl, using an electric hand mixer, beat together the eggs, coconut oil, vanilla extract, and coconut sugar until light and fluffy.
Stir in the coconut flour mixture, mixing well to ensure there are no lumps.
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 frosting.
In a large bowl, beat together the softened cream cheese and butter until light and fluffy.
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.
Spoon the icing into a parchment bag and swirl the icing on top of each cupcake.