Preheat your oven to 350°F. Line a baking sheet with a silicone baking mat or parchment paper and set aside.
Sift the flour, cocoa powder, and baking powder into a small mixing bowl. Whisk in the salt and set aside.
Add the eggs, brown sugar, and granulated sugar to the bowl of a stand mixer fitted with a whisk attachment. Beat the egg and sugar mixture for 3 to 5 minutes until light in color and doubled in volume.
Meanwhile, melt the semi-sweet chocolate with the butter in the microwave in a microwave-safe bowl at 20-second intervals until smooth.
Swap the whisk attachment for the paddle attachment and mix the melted chocolate into the egg mixture on medium speed (4-5 on a stand mixer) until combined and smooth. Make sure the chocolate is not hot before adding it to the eggs.
Mix in the flour mixture on medium speed until no more streaks of dry flour are visible, scraping down the bowl as needed to ensure everything gets incorporated. If using, mix in the chocolate chips.
Scoop out 1.5 tablespoon-sized balls of dough and place them on a lined baking sheet about 2 inches apart. Bake the cookies in batches for 10 to 12 minutes or until the edges are set and the tops are crackly. The centers will not look done when the cookies are removed from the oven. This is exactly what you want! The cookies will firm up as they cool.
Melt the white chocolate and shortening in a microwave-safe bowl at 20-second intervals in the microwave until smooth. Stir in the peppermint extract.
Dip the cooled cookies into the melted white chocolate halfway then sprinkle the crushed peppermint over top. Dip and sprinkle peppermint over one cookie at a time so the peppermint sticks to the white chocolate. Place the cookies on a flat surface to set. Transfer the cookies to the refrigerator to set quickly.