In a food processor, combine the eggs, agave, oil, applesauce, and yogurt. Pulse for 10-20 seconds. Using the shredder disk, shred the carrots into the egg mixture.
Transfer the carrot mixture to a mixing bowl. Add the flour, baking powder, baking soda, and cinnamon and mix with a hand mixer until all ingredients are combined, about 1 minute.
Spread the batter in a greased 8 x 11″ cake pan and bake 20-25 minutes, checking the center of the cake for doneness at 20 minutes. The cake will be very dense and should pull away from the sides of the pan when done.
While the cake cools, make the frosting: In a large bowl, use an electric mixer to beat the cream cheese and butter until smooth, about 2 minutes. Stir in the vanilla and powdered sugar, adding almond milk as needed to thin to your desired consistency.
When the cake is cooled, frost and serve.
Recipe by Love and Lemons at https://www.loveandlemons.com/?p=158