To make the frosting, blend all ingredients in your high-speed blender until smooth, adding as little water as possible. Taste it. Put in a bowl and set aside. 

To make the cake, cut the carrots into small chunks. Then throw all the ingredients (including the carrots) in your food processor and pulse until it's all in really small pieces and sticks together. 

Assembly: Press half the cake mix into the bottom of an adjustable spring-form pan, mine was about 6 inches. Then spread on about 1/3 of the frosting. Put it in the freezer until the layer of frosting is hard. Then press on the rest of the cake mix. I let it set in the fridge overnight, then frosted the whole thing, but you can do it right away if you want. Take it out of the pan and use the remaining frosting, cover with whatever garnishes you like.