Preheat oven to 350 degrees. Grease two 8-inch round cake pans, one baking sheet, or muffin tins with coconut oil.
Whisk together the coconut oil, coconut sugar, and eggs in a large bowl. In another bowl sift together the dry ingredients: the flour, baking powder, baking soda, cinnamon, and salt. Add the flour mixture to the egg mixture and stir to combine. Gently fold in the carrots with a spatula.
Divide the batter between the prepared pans or sheet pan and bake until a toothpick inserted comes out clean. About 25 minutes. Let cool 10 minutes in the pans on a cooling rack. If using 2 8-inch pans, after cooling 10 minutes, run a knife around the edge and remove cakes to cool completely on the rack.
For the frosting: In a large bowl beat ingredients until smooth. Spread over cake when cooled.