Heat oven to 350 degrees Fahrenheit and line two 9 inch round cake pans with strips of parchment paper for easy access. Wipe pans with coconut oil.
To prepare the cake batter, mix the flax eggs by adding the flax and water and set aside to thicken.
Meanwhile, add the oat flour, coconut flour, baking soda, baking powder, cinnamon, nutmeg, and date or coconut sugar to a large mixing bowl. Whisk to combine.
Add the prepared flax eggs, coconut cream, melted coconut oil, coconut milk, vanilla, and apple cider vinegar and stir to combine. Add the grated carrots and stir until well combined.
Pour the cake batter evenly into the two prepared cakes pans. Bake in the preheated oven for 35-37 minutes, until the cake is set in the center. Allow the cakes to cool completely.
To prepare the cashew frosting, add the soaked cashews, water, vanilla, date or coconut sugar, and maple syrup to a blender. Blend on high until the frosting is completely smooth.
Lay one cake on a serving plate or cake stand. Pour a layer of frosting over the bottom cake. Lay the second cake on top of the frosted bottom layer. Pour the remaining frosting over the top and swirl it evenly over the cake.
Let the cake set in the fridge before serving.
Store the cake in the fridge for up to one week.