Make the Cookie Dough: In a medium bowl, whisk together the flour, cocoa powder, baking soda, and salt.

In a large bowl, cream together the butter, granulated sugar, and brown sugar until light and fluffy.

Beat in the egg, peppermint extract, and vanilla extract until well combined.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined. Do not overmix.

Chill the Dough: Divide the dough in half, flatten into discs, wrap each disc in plastic wrap, and refrigerate for at least 1 hour (or up to 2 days).

Roll and Cut the Cookies: Preheat oven to 325°F (160°C). Line baking sheets with parchment paper.

On a lightly floured surface, roll out one disc of dough to about ⅛-inch thickness. Use a 2-inch round cookie cutter to cut out cookies.

Transfer the cookies to the prepared baking sheets, leaving about ½ inch between them.

Bake the Cookies: Bake for 8-10 minutes, or until the edges are set.

Cool the Cookies: Let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.

Melt the Chocolate: In a heatproof bowl set over a saucepan of simmering water (or in the microwave in 30-second intervals, stirring in between), melt the dark chocolate chips with the vegetable shortening (if using) until smooth.

Dip the Cookies: Dip each cooled cookie into the melted chocolate, coating completely. Place the dipped cookies back on the parchment paper-lined baking sheets.

Set the Chocolate: Refrigerate the cookies for about 15-20 minutes, or until the chocolate is set.