Cookie dough: In a mixer cream the butter until it is light and fluffy. Add the powdered sugar and continue to cream, scraping the sides of the bowl a couple times if necessary. Stir in the vanilla extract, salt, and cocoa powder. Mix until the cocoa powder is integrated and the batter is smooth and creamy, resembling a thick frosting. Add the flour and mix just until the batter is no longer dusty looking but still a bit crumbly. Turn the dough out onto a clean counter, gather it into a ball, and knead it together into a nice, smooth mass. Divide the dough in 2, flatten into disks, and wrap in plastic wrap. Chill for 15 minutes.
Rollout and bake: Preheat oven to 350. Roll dough out really thin, about 1/8-inch. These are called thin mints after all. You can either roll it out between two sheets of plastic, or dust your counter and rolling pin with a bit of flour and do it that way. If the dough is too firm to roll you can microwave it for 5 seconds. Cut out cookies and bake for 10 minutes. Remove the cookies from the oven and allow them to cool completely on a wire rack.
Make the peppermint coating: Meanwhile, prepare your chocolate coating. Using a double boiler, slowly melt the chocolate, stirring occasionally until it is glossy and smooth. You can add 1 tablespoon of shortening if your chocolate is too thick. Alternatively, use a microwave in short 15-20 second bursts to melt the chocolate. Stir in the peppermint extract if you don’t have the mint candy melts.
Finishing the cookies: Using a fork gently drop the cookies one at a time into the chocolate coating. Flip to coat all sides. Lift the cookie out of the chocolate with the fork and bang the fork on the side of the pan to drain any extra chocolate off the cookie. You are after a thin, even coating of chocolate. Place on a parchment lined baking sheet, and repeat for the rest of the cookies. Place the cookies in the refrigerator or freezer to set.