Prepare the dough: Sift together the cocoa powder, flour and salt in a large bowl.
Using a mixer, cream the butter and sugar. Add the eggs one at a time, then the vanilla, incorporating each ingredient before adding the next. Add the dry ingredients and mix just until incorporated, scraping the bottom of the bowl with a rubber spatula.
Divide the dough into 2 pieces; place one piece between 2 lightly floured sheets of parchment paper and roll into a 1/4-inch-thick rectangle. Repeat with the other piece of dough. Refrigerate both rectangles, covered with the parchment sheets, until firm, at least 1 hour or up to several days.
Using a 2-inch round cutter, cut the dough into 64 circles. (You can reroll the scraps once.) Place the cookies about 2 inches apart on ungreased baking sheets and chill for 20 minutes. Preheat the oven to 325 degrees.
Bake the cookies until they are set and slightly darker around the edges, about 20 minutes. Cool completely on wire racks.
Meanwhile, prepare the filling: Using a mixer, cream the butter and shortening until fluffy. Beat in the confectioners' sugar and vanilla.
Flip half of the cookies upside down and top each with 1 level tablespoon of filling. Press the remaining cookies on top to make sandwiches.