Preheat the oven to 350 degrees F and grease a jelly roll pan (15 x 10 inches). Set aside.
Mix the ground flaxseed and water in a small bowl and set aside to make your flax eggs.
In a large bowl, whisk together the pumpkin puree, coconut oil, sugar and flax eggs until smooth.
Now add the flour to the wet ingredients. Sprinkle the baking powder, baking soda, cinnamon, nutmeg and salt on top of the flour and mix with a large spoon until just combined.
Pour into the prepared pan and smooth out evenly. Bake for 25-30 minutes, until a toothpick inserted into the middle comes out clean. Let the cake cool completely before frosting.
Make the Frosting: Using a hand mixer, beat the softened vegan butter for about 2 minutes until creamy, then add the powdered sugar, apple cider vinegar and vanilla and beat everything together until smooth and creamy, adding a tablespoon of non-dairy milk at a time as needed. If you add too much milk and it gets runny, you will need to add more powdered sugar.
Once the cake is cooled completely, frost the cake, cut into bars and serve. Enjoy!