Make the dough:
Sift the flour, cocoa powder, and salt together into a bowl. Set aside.
Put the butter and sugar in the bowl of a stand mixer fited with the paddle attachment. Beat on medium speed just until combined. Add the vanilla extract.
Switch the mixer to low speed and add the dry ingredients in 3 additions, pulsing the mixer to incorporate each addition before adding the next one. The dough will look dry.
Turn the dough out onto a lightly floured work surface. Knead a few times just until it comes together. Flatten into a disk, wrap in plastic wrap, and refrigerate until firm, at least 3 hours or up to 2 days.
Bake the cookies:
Preheat the oven to 325°F. Line the bottoms of two 12-by18-inch sheet pans with parchment paper.
Remove the dough from the refrigerator and unwrap it. On a lightly floured work surface, roll out the dough 1/8 inch thick. Using a 1 1/2 inch round cookie cutter, set out as many rounds as possible. Reroll the scraps only once, using less flour on the work surface to prevent toughness, and cut again. You should have 60 rounds in all. Place the rounds on the prepared pans, spacing them 1/2 inch apart.
Bake on the middle shelves of the oven, rotating the pans 180 degrees halfway through the baking time, until the tops are lightly cracked and hold a slight indentation when pressed with a fingertip, about 10 minutes. Let cool completely on the pans on wire racks.
Store in an airtight container at room temperature until you are ready to assemble the sandwiches.
Make the filling and assemble the cookies:
Put the chocolate in a medium bowl.
Put the cream and powdered sugar in a small saucepan and bring to a simmer over medium heat. Cook at a simmer for 1 minute and remove from the heat.
Pour the hot cream mixture over the chocolate. Whisk the mixture by hand until the chocolate melts. Whisk in the butter, and then the vanilla extract.
Pour the truffle cream into a bowl, cover with plastic wrap so that the wrap is touching the surface, and refrigerate until the consistency of thick mayonnaise, 30 to 45 minutes.
Arrange half of the cookies, bottom side up, on a sheet pan. Put the truffle cream into a pastry bag fitted with a ¼-inch star tip and pipe a swirl of the cream onto the top of each cookie, distributing the cream evenly among them. Top each covered cookie with a second cookie, bottom side down, and press gently to adhere it to the truffle cream. Store in a cool place until serving.
Just before serving, sift a dusting of cocoa powder on the tops of the cookies. Transfer to a serving plate.