Preheat your oven to 375 degrees, line a baking sheet with Silpat, parchment paper, or cooking spray, and set it aside.
Make your vegan buttermilk by taking a liquid measuring cup, adding 1 cup of non-dairy milk with 1 TB vinegar, stirring until combined, and setting it aside. Make your flax egg by combining your 1 TB flax meal with 2 TB water in a small cup, mixing, and letting it thicken.
Take a stand mixer fitted with the paddle attachment or a hand mixer with a large mixing bowl. Add the shortening and white and brown sugar, and mix on medium for a few minutes until it starts to get creamy. Then add the vanilla extract, flax egg, cocoa powder, baking soda, and salt; stir until combined. Then add the 2 cups of flour and vegan buttermilk until combined.
Let the batter rest for about 5 minutes.
Take your prepared cookie sheet and a small to medium cookie scoop and scoop out the batter; these will spread, so don't put them too close together; 12 worked on my cookie sheet.
Bake for 8-10 minutes, don't overbake. Let rest for 5 minutes, then place them on a cooling rack to cool.
Take your stand mixer and a clean bowl and combine the filling ingredients; mix slowly, then medium-high until whipped well for a few minutes.
Match up the cookies in twos, take the bottom half, and spread frosting on the flat part, then place the unfrosted pair (flat sides together) to make a sandwich. Repeat with the remaining cookies.