Set two racks in the middle of the oven. Preheat to 375 degrees.
In a food processor, or bowl of an electric mixer, thoroughly mix all dry ingredients for the cookies. On low speed, or while pulsing the processor, add the butter, and then the egg.
Continue processing or mixing until dough comes together in a mass. It will be a very stiff, very dry dough; this is what it's supposed to look like.
Take rounded teaspoons of batter and place on a parchment paper-lined baking sheet approximately 2 inches apart. With moistened hands, slightly flatten the dough. Bake for 9 minutes, rotating once for even baking. The cookies will look puffy; that's okay. Set baking sheets on a rack to cool and thump them slightly to make the cookies "deflate" (or press them down with the back of a spoon).
To make the filling, place butter and shortening in a mixing bowl and, at low speed, gradually beat in the sugar and vanilla. Turn the mixer on high and beat for 2-3 minutes until filling is light and fluffy.
To assemble the cookies, pipe a blob of cream into the center of one cookie. Place another cookie, equal in size to the first, on top of the cream. Lightly press, to work the filling evenly to the outsides of the cookie.