Set 2 racks in the middle and upper third of the oven and preheat to 375 degrees. In a food processor or the bowl of an electric mixer, thoroughly mix together the flour, cocoa, baking soda, baking powder, salt and sugar. While pulsing or on low speed, add the butter, then the egg. Process or beat until the dough is thoroughly blended and massed together. Drop rounded teaspoons of batter onto nonstick or 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. Set 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 up to high and beat for 2 or 3 minutes more, until fluffy.

With a pastry bag fitted with a 1/2-inch tip, pipe teaspoon size blobs of filling onto the tops of half 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.