Shred carrots with attachment of a food processor or box grater. Zest lemon and orange and squeeze juice from half of each. Place carrots, lemon, orange, and remaining ingredients in a food processor and pulse until combined. Divide into 4 small ramekins using 4 tablespoons each.
Place frosting ingredients into a blender. Add 2 tablespoons water and blend. Scrape down sides and add more water to make a very thick, smooth texture.
Frost cakes and sprinkle with cinnamon. Store covered in refrigerator.