Preheat oven to 375 degrees. Line two large baking sheets with parchment paper; set aside. Sift together flour, cocoa, baking soda, and salt into a small bowl; set aside.
Add butter, shortening, and sugars to the bowl of an electric mixer fitted with the paddle attachment; cream on high speed until smooth, about 3 minutes. Add egg; beat until pale and fluffy, about 2 minutes. Add half the flour mixture, then the milk and vanilla; beat until combined. Add the remaining flour mixture. Beat together, scraping down sides of bowl with a rubber spatula as needed.
Drop 12 slightly rounded tablespoons of batter 2 inches apart on each baking sheet. Bake the cookies in the upper and lower thirds of oven, 10 minutes; switch the positions of the baking sheets, and rotate each one. Continue baking until the cookies spring back to the touch, 2 to 4 minutes more.
Remove from oven; let cookies cool on baking sheets, 10 minutes.Transfer with a metal spatula to a wire rack; let cool completely. Meanwhile, line a cooled baking sheet with a new piece of parchment; repeat process with remaining batter.
Spread 1 scant tablespoon buttercream on flat sides of half the cookies.Top each with one of the remaining cookies, flat side down, and gently press together. Transfer pies to a tray.
Melt half the chocolate in a saucepan over low heat, stirring until smooth. Remove from heat; add remaining chocolate, and stir until melted and smooth. Transfer to a pastry bag fitted with a plain round tip (Ateco #2 or #3) or a small parchment cone. Pipe chocolate in a spiral pattern on top of each pie. Let chocolate set before serving, about 1 hour.