Preheat oven to 350 degrees. Coat two 9" round cake pans with coconut oil spray.
Use a food processor to grate the carrots.
Whisk together the shredded carrots, eggs, sugar, oil, buttermilk, and vanilla extract.
In another bowl, combine together the flours, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and clove until mixed well.
Add the flour mixture into carrot mixture until well combined.
Distribute batter evenly between the pans and place into the oven. Bake for 30-40 minutes or until cake tester comes out clean. Allow cakes to cool completely before icing.
To make the frosting, place one stick of butter in a small saucepan. Cook on medium-high heat until butter is browned, about 5 minutes. Pour through a small sieve into a small bowl to remove any brown bits then place into the refrigerator for 15 minutes to cool. Once cooled, cream together browned butter, regular butter, cream cheese, vanilla extract, and salt with a beater until smooth.
Add powdered sugar one cup at a time, beating well between each addition. After 2 1/2 cups, taste to see if additional sugar is necessary. I only used 2 1/2 cups.
Place bottom layer of cake on cake stand, leveling the top if necessary. Add a layer of icing. Place second layer on top, leveling if necessary. Dirty ice the cake (click link up above for directions). Place in refrigerator for 20 minutes to chill. Finish icing the rest of the cake using an offset spatula.
Garnish the bottom of the cake with toasted coconut and sprinkle some on top evenly. Refrigerate. Serve cake at room temperature. Enjoy!