Preheat oven to 175 Celsius (350 Fahrenheit) and line or grease 9x5 inch loaf tin. Set aside.
With the shredding blade attached to the food processor, shred carrot. Empty out carrot into a mixing bowl and attach a normal blade to the food processor.
Combine soy milk, vegetable oil, flaxseed meal, brown sugar, cane sugar, vanilla extract, ground cinnamon and ground ginger in the food processor. Process till smooth, about 30 seconds.
Add cake/pastry flour, baking soda and baking powder into food processor and pulse till almost everything is mixed up.
Remove food processor lid and using a spatula, give your cake batter a manual stirring. Once just combined, pour batter into the bowl that contains your shredded carrot.
Stir until combined and then mix in chopped walnuts.
Scrape mixture into prepared loaf tin and bake for 45-60 minutes, or until a skewer comes out clean. Check at the 45 minute mark first, and continue baking if cake is still not cooked.
Once baked, leave to cool for 10 minutes and then remove from tin and leave to thoroughly cool on a wire rack.
Prepare your frosting by mixing Earth Balance, Tofutti, zest of 1 orange and vanilla extract with an electric mixer till light and fluffy.
Add sugar in and continue whipping till light and sugar has dissolved.
Top cooled cake with prepared icing.