Preheat the oven to 350°F (180°C). Spray a 9x13 inch pan with non-stick spray and set aside. For layer cake instructions see notes*.
Sift the flour into a mixing bowl and add the white and brown sugar, baking powder, baking soda, salt and cinnamon and mix together.
Prepare the vegan buttermilk by placing 1 Tbsp of lemon juice into a measuring jug and then adding soy milk up to the ⅔ (160ml) line. Allow to sit for a minute to curdle.
Add the bananas, vegan buttermilk and coconut oil to a blender jug and blend briefly until combined. Don't overblend.
Pour the blended bananas, buttermilk and coconut oil over the dry ingredients and mix in.
Prepare your flax egg by mixing 1 Tbsp flaxseed meal with 3 Tbsp Hot Water and allowing to sit for a minute to become gloopy.
Add the flax egg, applesauce and vanilla extract and whisk briefly with a hand whisk to remove any lumps.
Pour the batter out into the prepared 9x13 pan and spread out evenly.
Place into the oven and bake for 40 minutes or until a toothpick inserted into the center comes out clean.
Place the whole sheet pan onto a cooling rack and leave it to cool completely before frosting.
Prepare your frosting by adding the powdered sugar, vegan butter and 2 tablespoons of lemon juice to the bowl of your stand mixer and starting at slow speed, gradually increase speed until perfectly thick and smooth. If the frosting is too thick, add the remaining lemon juice a drop at a time until you get the right consistency.
Frost the cooled cake, and decorate with crushed walnuts.