In the bowl of an electric mixer, thoroughly mix together the flour, cocoa, baking soda, baking powder, salt, and sugar.
While mixing on low speed, add the butter, then the egg. Beat or process until the dough is thoroughly blended and massed together.
Drop rounded teaspoons of batter onto parchment-lined cookie sheets at 2-inch intervals. With moistened fingers, round out the cookies and flatten them a little.
Bake for 9 minutes, turning the pans once for even baking, until the cookies are set. Sit the cookie sheets on a rack to cool.
Vanilla Cream Filling:.
Put the butter and shortening in a mixing bowl and, at low speed, gradually beat in the confectioners' sugar and vanilla, until blended.
Turn the mixer speed to high and beat for 2-3 minutes more, until fluffy.
To assemble, place teaspoon size blobs of filling onto the tops of half of the cookies. Keeping the smooth bottoms of the cookies facing up, flip the remaining cookies on top of the filling and lightly press to form sandwiches.