Preheat oven to 375 degrees. Set rack in middle. In mixing bowl, thoroughly mix the flour, cocoas, baking soda, baking powder, salt and sugars. After combined, on low speed, add the butter then the egg. Continue mixing until dough comes together in a mass (about 3 minutes). Place 2 tsp. of batter on a parchment lined baking sheet, about 2 inches apart. With the bottom of a glass slightly flatten the dough. Bake for 9 minutes, rotating once. Set on baking racks to cool.
For filling, mix butter and shortening on low speed, gradually beating in the sugar and vanilla. When combined, turn mixer on high and beat for 2-3 minutes until light and fluffy. To assemble cookies, put filling in a gallon zip top bag. Squeeze all filling to one corner, and cut off the corner of bag. Pipe about 1 tsp. of filling into the center of one cookie. Sandwich with another cookie and enjoy!