Set rack in the middle of the oven and preheat to 375 degrees F.
In a food processor or the bowl of an electric mixer, thoroughly mix together the flour, cocoa, baking soda, baking powder and salt. On low speed, add the butter, then the egg and vanilla. Process or beat until the dough is thoroughly blended and massed together.
Drop rounded half teaspoons of batter onto a non-stick cookie sheet at 2-inch intervals. With moistened fingers, round out the cookies and flatten them a little. Bake for 8 minutes, turning once for even baking, until the cookies are set. Cool on the pan on a rack.
To assemble the cookies, place 1/2 of the cookies, top side down on a flat surface. Scrape the cream filling into a pastry bag fitted with a 1/2-inch star tip. Pipe teaspoon sized rosettes of the filling on the tops of the cookies. Place the remaining cookies, top side up on top of the filling and lightly press to form sandwiches.
Place the butter and shortening in the bowl of an electric mixer and beat until combined. Gradually beat in the vanilla and confectioners' sugar at low speed until blended. Increase the speed to high and continue beating for 2 to 3 minutes until fluffy.;