Preheat your oven to 350 °F and grease a 9 inch cake pan. Set aside.
In a small bowl, prepare your flax egg by whisking together 1 tablespoon of ground flaxseed with 3 tablespoons of warm water. Set the mixture aside to thicken.
In a mixing bowl, cream together the vegan butter and sugar. Then add in the thickened flax egg and vanilla and mix until combined.
Add in the remaining dry ingredients and stir until combined. Fold in the chocolate chips.
Pour the dough into your prepare cake pan and press it down until it's a uniform layer.
Bake the cookie cake for 22-25 minutes or until slightly golden.
Allow the cookie cake to cool while you prepare the frosting.
To make the frosting, simply use a food processor with the dough attachment or a hand mixer to beat all the ingredients together until smooth. Only add non-dairy milk--a teaspoon at a time--as needed.
Once the cake has cooled, frost the cookie however you desire. Top with some chocolate shavings or sprinkles and enjoy!
Notes
*You can also use coconut sugar instead of brown sugar.