Preheat oven to 350 degrees F and grease an 8-inch square baking pan.
In a large mixing bowl, cream vegan butter and sugar until light and fluffy. In a tall glass, whisk together Egg Replacer, water, coconut milk, and vanilla until foamy. Add the Egg Replacer mixture to the creamed butter and sugar and beat together with a hand mixer until thoroughly combined. In a separate bowl, combine flour, baking soda, salt, and cinnamon. Add the dry ingredients to the wet ingredients and beat together. Batter will be thick. Using a large spoon, stir in apples and walnuts.
Spread the batter into the prepared baking pan and bake for 35-40 minutes until a toothpick inserted near the center comes out clean and cake begins to pull slightly from the edges of the pan. Can be served warm with So Delicious(R) Dairy Free Coconut Milk ice cream or whipped topping, or at room temperature on its own.