Mix the soy milk and the apple cider vinegar and set aside in the fridge.
Blend the flax seeds and 3 tablespoon water in a small bowl and also set this aside into the fridge.
In a big bowl sieve the flour and baking powder with the baking soda, cinnamon and ginger powder.
In another small bowl combine the brown sugar with the vanilla extract and coconut oil and add it to the flour mixture. Also, mix in the shredded carrots as well as the milk/vinegar and flaxseed mix. Stir well to combine everything into your cake batter.
Divide the batter between two equally sized, lightly greased baking tins (about 17.5cm diameter). In case you do not have 2 tins of the same size, simply bake the layers one after another and let them both cool down completely before going to the next step.
Let's get to the cream filling and topping for the carrot cake: Simply blend the melted coconut oil with the rest of the ingredients into a smooth and creamy texture. If needed, even out your bottom layer, so the top can sit comfortably on it without sliding off, then use a large pallet knife to spread about half of the creamy mixture onto the bottom layer, then cover with the second layer. Repeat until the creamy mixture is all used up.
Of course, you can now decorate the carrot cake - how about some pecans or shredded coconut? You can also add some more shredded carrot as I have done on my photo above.