Combine butter and sugar in a large bowl (or the bowl of a stand mixer) and use an electric mixer to beat until creamy and well-combined.
Add egg and stir well.
Stir in extracts.
In a separate, medium-sized bowl, whisk together flour, cocoa powder, baking powder, and salt.
Gradually add dry ingredients to wet, stirring until well-combined (be sure to scrape the sides and bottom of the bowl so that all ingredients are evenly incorporated).
Divide the dough into two parts and form each into a disk, flattening each to about 1" thick. Cover in plastic wrap and chill for at least 1 hour.
Once dough has chilled, preheat oven to 350F (175C) and prepare cookie sheets by lining with parchment paper. Set aside.
Transfer dough to a clean, lightly floured surface and sprinkle flour over the top. Use a rolling pin to roll dough to about ⅛-⅙" thickness (yes, you want it to be pretty thin!).
Using a 1 ¾" round cookie cutter and cut out circles, transferring each to cookie sheet (the cookies won't spread so you can place them about ½-1" apart).
Once you have cut out all of the circles that you can, be sure to re-combine the scraps and roll out and cut out again to get the maximum number of cookies from your dough.
Bake on 350F (175C) for 8-9 minutes and allow cookies to cool completely before dipping.
Mint Chocolate Coating
Melt one 10oz package of melting wafers in a microwave-safe bowl according to package instructions.
Once melted, set aside and in a separate, small bowl, combine 1 teaspoon of shortening and ¼ teaspoon of peppermint extract. Microwave until shortening is melted.
Pour shortening and extract mixture into melted chocolate and stir until well-combined.
Place one baked, cooled cookie on the tongs of a dipping fork (I use the fork from this set (affiliate), but a regular kitchen fork would work in a pinch!) and dip in chocolate. Lift out of chocolate and try to drain off as much as possible, transfer covered cookie to wax paper lined surface to cool completely. If using sprinkles, decorate immediately as the chocolate sets rather fast.
Once you've used all of your chocolate, repeat with second set of melting wafers/shortening/extract.
Allow chocolate to harden before serving.