Decorative gluten-free sprinkles(optional for topping)
Lightly grease a 9-inch Bundt pan with coconut oil and dust with 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.
In a large mixing bowl, combine coconut oil, agave, apple sauce, sugar, salt, baking soda, baking powder, cinnamon, ginger, almond milk, and chia mixture. Whisk to combine. Add grated carrot and flours and mix to combine. (Batter should resemble a normal batter consistency; if too thick, add splashes of additional almond milk. Mine was perfect using the recommended ¾ cup almond milk.) Pour in chopped walnuts and stir.
Preheat the oven to 350°F. Pour batter into the Bundt pan and bake for 40-50 minutes, or until a toothpick inserted comes out clean. Remove from oven and let cool for at least 15 minutes before flipping the cake to remove from pan.
While the cake cools, make the icing. In a blender, add soaked and strained cashews, coconut milk, vanilla, agave, lemon juice, vinegar, and salt. Blend or pulse to combine. Slowly pour in 4-6 tablespoons almond milk until icing blends into a smooth, creamy, and pourable mixture. (I used 6 tablespoons almond milk total.)
Gently pour the icing over the cake, using enough to coat the cake as desired (I used about ¾ of the icing mixture). Top cake with chopped walnuts and decorative sprinkles, if desired. Slice cake and serve with remaining icing.