Lightly oil and flour a 9-inch bundt pan with coconut oil and dust with gluten-free flour. Shake out excess flour and set aside.
Combine ground chia and water in a bowl. Whisk to combine. Wait at least 10 minutes for consistency to become egg-like.
Melt coconut oil in a saucepan and add to a large mixing bowl. Add agave, apple sauce, demerara sugar, sea salt, baking soda, baking powder, cinnamon, ginger, almond milk and chia egg. Whisk to combine.
Add grated carrot, almond flour and gluten-free flour and mix to combine. (Batter should resemble a normal batter consistency, if too thick add splashes of more almond milk. Mine was perfect using the recommended 3/4 cups almond milk). Finally pour in chopped walnuts and stir.
Preheat oven to 175C/350F. Pour batter into bundt pan and bake for 45-55 minutes, or until a toothpick inserted into the cake comes out clean. Remove from oven and let cool for at least 15 minutes before flipping the cake to remove from pan.
While you’re waiting for the cake to cool make your icing. In a blender add soaked cashews (strained), canned coconut milk, vanilla extract, agave, lemon juice, apple cider vinegar, and pinch salt. Blend or pulse to combine. Then, slowly pour in 4-6 tbsp almond milk until cashew icing blends into a smooth, creamy and pourable mixture. (I used 6 tbsp almond milk total).
Gently pour icing over cake using enough to coat cake as desired (I used about 3/4 of the icing mixture). Optional to top cake with chopped walnuts. Slice carrot cake and serve with remaining vanilla cashew icing.