Position a rack in the center of the oven and preheat the oven to 375 degrees. Line two baking sheets with parchment paper.
Sift together the flour, cocoa powder, baking soda, and salt onto a sheet of waxed paper. In the work bowl of a stand mixer fitted with the paddle attachment, beat together the butter, shortening, and brown sugar on low speed until just combined. Increase the speed to medium and beat until fluffy and smooth, about 3 minutes. Add the egg and vanilla and beat for another 2 minutes.
Add half of the flour mixture and half of the milk to the batter and beat on low until just incorporated. Scrape down the sides of the bowl. Add the remaining flour mixture and ½ cup milk and beat until completely combined.
Using a spoon, drop about 1 tablespoon of batter onto one of the prepared baking sheets and repeat, spacing them at least 2 inches apart. Bake one sheet at a time for about 10 minutes each, or until the pies spring back when pressed gently. Remove from the oven and let the cakes cool on the sheet for about 5 minutes before transferring them to a rack to cool completely.
While the cakes are cooling, make the marshmallow filling. To assemble the pies, spread the filling on the flat side of one cake and top it, flat-side-down, with another cake.
Roll the edges in sprinkles, if desired.