Whisk together flour, cocoa powder, baking powder, and salt in a large bowl.

Reduce speed to low and gradually add flour mixture; beat just until incorporated.

Divide dough in half and use damp hands to shape each portion into a 10-inch log.

Wrap in plastic and refrigerate until very firm, about 2 hours (rotate dough occasionally while chilling to prevent flat sides).

Preheat oven to 350°F and line two baking sheets with parchment paper.

Use a sharp knife to cut logs into slices (just shy of 1/4-inch thick), rotating rolls to keep them from flattening.

Bake for 9 minutes, until edges are set.

Cool for 2 minutes on baking sheets, then transfer cookies to a wire rack to cool completely.

While cookies cool, place chopped chocolate in a double boiler, or in a heat-proof bowl over a saucepan of gently simmering water. Slowly melt the chocolate, stirring occasionally until glossy and smooth. Stir in peppermint extract and reduce heat to low so that coating will retain its consistency. Line two baking sheets with parchment paper.

Drop cookies into the melted chocolate mixture one at a time to fully coat.

Lift the coated cookies out of the chocolate with a fork, tapping fork gently against the bowl to allow excess chocolate to drain off. Place coated cookies on prepared baking sheets and freeze or refrigerate until set (about 15 to 20 minutes).

Store leftover cookies in an airtight container in the refrigerator or freezer.