To begin, preheat your oven to 350 and spray a 9x13 pan with non-stick spray.
To a large mixing bowl, add your butter, Greek yogurt, applesauce, white sugar and brown sugar and beat together with a mixer till smooth. Add your eggs and vanilla and mix together till the eggs are well incorporated.
To the same bowl, add your almond flour, oat flour, gluten-free all purpose flour, baking soda, baking powder, cinnamon, ginger, nutmeg and salt. Stir together till you have a consistent cake batter.
Add your carrots, coconut and walnuts and fold them into the cake batter till they're evenly incorporated. Pour into your 9x13 pan in an even layer.
Bake in the oven for 40-45 minutes, or till a toothpick inserted into the center of the cake comes out clean. Let cool entirely before frosting.
To a mixing bowl, add your butter and cream cheese and beat together with a mixer till smooth.
To the same bowl, add your vanilla, cinnamon and 1 cup of powdered sugar. Beat until thick and creamy. Add another cup of powdered sugar and beat again till creamy and smooth.
Spread on top of your cooled cake in a thin, even layer. Decorate the top with sprinkles, nuts, carrots, coconut, etc.
Devour!
Stored in an airtight container in the fridge, this cake tastes best within a week.