Preheat your oven to 350 degrees. Get a baking sheet lined with a Silpat and set it aside.
Make your flax egg and set it aside. Take a stand mixer and add your vegan butter, sugars, plant milk, and vanilla extract- mix until creamed. Then add your flax eggs and mix until combined. Add your salt, baking powder and mix until combined, now add your flour and oats, mix until combined. Take your cookie scoop and scoop out your dough *it's fairly thick* and place it on the cookie sheet, flatten the cookie a bit; it will not spread in the oven. And repeat with the remaining dough. Cook in the preheated oven for 8-10 minutes; they should be slightly firm but still soft- they will cook some more on the cookie sheet. Let rest for 5 minutes on the cookie sheet and then transfer to a cooling rack.
Make your filling. Take a hand or stand mixer, whip all ingredients until smooth. Set aside.
When your cookies are completely cool, you can take two cookies of like size, put some filling on one of the bottom sides of the cookies (the amount will vary on how much you would like), and then sandwich the backside of the other cookie together. These may need to go in the fridge until serving; the frosting likes to melt on warm days. They taste great right out of the fridge.