Preheat oven to 350 F.
Whisk flour, baking powder, baking soda, and salt together in a medium size bowl.
Add vinegar to soymilk to sour and set aside.
Mix ground flax seed with water and let set for about 5 minutes to gel.
Cream shortening (or vegan butter) until light
Add sugar to shortening and blend very well until light and fluffy.
Add flax and water mixture, and vanilla to shortening and sugar and mixture.
Add 1/3 of the flour mixture into the wet mixture and stir to incorporate. Then add 1/2 of the soymilk mixture, and stir. Then add 1/2 of the dry mixture, then the rest of the milk mixture, and then the last of the flour mix, stirring to incorporate the mixture together after each addition.
Drop 1/4 cup for each cookie onto parchment paper lined cookie sheet. Cookies will spread so leave at least 3 inches between each cookie.
Cook for about 18-20 minutes until a light golden brown.
Cool on a wire rack.
When cooled, frost the bottoms (flat side of cookie) with 1/2 vanilla. Let dry for about 30 minutes. Then frost the other half of the cookie with chocolate icing.
Store in an air-tight container for up to 3 days. Can freeze.