Position rack in center of oven; preheat to 375ºF. Line two baking sheets with parchment paper.
Sift together flour, cocoa powder, baking soda, and salt on a sheet of waxed paper. In the work bowl of a stand mixer fitted with the paddle attachment, beat butter, shortening, and brown sugar on low until just combined. Increase speed to medium; beat for 3 minutes. Add egg and vanilla; beat 2 more minutes.
Add half of flour mixture and half of milk to batter; beat briefly on low. Beat in remaining flour mixture and milk.
Using a spoon, drop batter 1 Tbsp at a time onto one of the baking sheets, spacing at least 2 inches apart. Bake one sheet at a time for about 10 minutes, or until pies spring back when pressed gently. Remove from oven; let pies cool on sheet for 5 minutes; transfer to a rack to finish cooling.
To make filling: Beat Fluff and shortening for 3 minutes on medium. Reduce speed to low, and add sugar and vanilla. Beat until incorporated. Increase speed to medium; beat until fluffy.
Sandwich filling between the flat sides of two pies; repeat.