Preheat the oven to 180 degrees C/350 degrees F and lightly grease 3 8-inch cake tins with vegan butter.
To a large mixing bowl, add the rice flour, buckwheat flour, coconut sugar, cinnamon, chickpea flour, baking powder, xanthan gum, and ground ginger. Stir together well.
To a different bowl, add plant based milk, olive oil, apple cider vinegar and grated carrots, and mix together.
Add the wet ingredients to the dry together with a flax egg. Mix together until well-combined. The batter should be on the thicker side, but still easy to pour.
Pour an equal amount of batter into the cake tins and bake in the preheated oven for 25-30 minutes, until golden brown and a toothpick comes out clean from the centre.
When the cakes are ready, transfer them to a cooling rack and allow to cool fully either in the fridge or on the counter before adding the frosting.
To make the frosting, add the vegan butter, icing sugar, orange juice and vanilla extract to a large mixing bowl. Use a handheld or stand mixer to whisk until very smooth. I would recommend leaving the frosting in the fridge for 15 minutes to firm up.
Add a thick layer of the frosting to one of the cake sponges, then place the second cake sponge on top. Repeat the process once more, finishing with a layer of frosting on top of the cake.
Make sure that the cake sponges cool down fully before adding the frosting. I would recommend allowing them to chill in the fridge for best results.
If you want to, you can add chopped nuts of your choice, such as walnuts or pecans.
For a more fluffy texture, reduce the amount of carrots used by half.
I would recommend weighing the ingredients for the best results. See the recipe card for an automatic conversion to metric amounts of each ingredient.