In a bowl, mix the dry ingredients - flour, baking powder, baking soda and spices.
In a separate bowl whisk eggs. Add melted but cooled coconut oil, honey and vanilla. Mix well.
Add dry ingredients to wet ingredients and mix thoroughly. Stir in grated carrot and mix well with a spoon. Add milk if the mixture is too thick.
Pour the mixture into the baking pan and bake for 25-30 minutes (check with a toothpick, if it comes out clean the cake is ready). Remove from the oven and allow to cool. During that time, prepare the frosting.
Mix all ingredients with the electric mixer until the mixture is smooth.
Let the mixture set for 20 minutes in the fridge.
Spread on top of the cooled cake.
Keep in an airtight container refrigerated until serving.