Place rack in center of oven and preheat to 375.
Lightly grease whoopie pan cavities.
Sift together the flour, cocoa powder, baking soda, and salt onto a sheet of waxed paper.
In the work bowl of a stand up 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 a 1/2 cup of milk to the batter and beat on low until just incorporated. Scrape down the sides of the bowl. Add the remaining flour and 1/2 cup of milk and beat until completely combined.
Using a spoon, drop about one tablespoon of batter into each cavity. 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 cooling rack. Cool completely.
In the work bowl of a stand mixer with the paddle attachment, beat together the peanut butter and butter on low speed until smoothy and creamy. Add the confectionery sugar and the sals and beat on low to incorporate. Increase the speed medium and beat until the filling is light and fluffy, about 4 minutes.
Frost whoopie pies and enjoy!
Note: This frosting is pretty salty, so feel free to cut back if necessary.