In a large bowl add soy milk and a flax meal. Set it aside for about 5-10 minutes.
After a few minutes add vanilla, brown sugar, and melted coconut oil, and combine.
Next, add oat flour, buckwheat flour, rice flour, ground walnuts, baking powder, baking soda, and salt. Carefully combine and create a smooth dough. If needed add 2 tbsp of milk. The consistency should be thicker but creamy.
Lastly, add shredded carrots and cinnamon, and lightly combine.
Pour the batter into a square baking pan (9" or 22cm) and bake at 350F (180C) for 45 minutes.
Meanwhile, prepare coconut frosting by cooking cornstarch with coconut milk. Bring it to a boil and whisk until very thick. Set it aside and cool it down.
When the cornstarch mixture is cooled down, move to the next step. In a medium-sized bowl add softened vegan butter and sugar. Whisk until fluffy and slowly add the cornstarch mixture. Whisk until combined and airy.
When the carrot cake is completely baked and cooled down decorate it with coconut frosting. Enjoy!