Melt the chocolate: Place the semisweet chocolate chips in a microwave-safe bowl. Microwave in 20-second intervals, stirring thoroughly between each, until almost completely melted. Stir until smooth and let cool for about 5 minutes. The chocolate should be fluid but not hot.
Cream the butter and sugars: In a large bowl, beat the softened butter, granulated sugar, and brown sugar with an electric mixer on medium speed for about 2 minutes, until lighter and creamy. Scrape down the sides of the bowl as needed.
Add the eggs and flavorings: Beat in the eggs one at a time, mixing until incorporated after each addition. Add the peppermint extract and vanilla extract. The mixture may look slightly loose, which is normal.
Add the melted chocolate: Pour in the cooled melted chocolate and mix on low speed just until evenly combined. The dough should become noticeably darker and thick.
Combine the dry ingredients: In a separate bowl, whisk together the flour, cocoa powder, baking powder, and kosher salt. Gradually add the dry ingredients to the chocolate mixture and mix on low speed just until no dry streaks remain. Do not overmix.
Fold in peppermint candy: Fold in 1/4 cup of the crushed peppermint candies, reserving the remaining 1/4 cup for topping. The dough will be soft and somewhat sticky.
Chill the dough: Cover the bowl and refrigerate for 30 minutes. The dough should become scoopable and thick enough to hold a rounded shape. If it is still unusually loose, chill for another 10–15 minutes.
Prepare the oven and baking sheets: Heat the oven to 350°F (175°C). Line two rimmed baking sheets with parchment paper. Scoop the dough into approximately 1 1/2-tablespoon portions and place them about 2 inches (5 cm) apart. Gently round the portions if needed.
Bake the cookies: Bake for 9–11 minutes, one baking sheet at a time, until the edges look set but the centers still appear soft and slightly glossy. Do not wait for the centers to look completely dry; that will make the cookies less fudgy.
Add the peppermint topping: Immediately sprinkle the remaining 1/4 cup crushed peppermint candies over the warm cookies, gently pressing a few pieces into the surface if necessary. Let the cookies cool on the baking sheet for 5 minutes before transferring them to a wire rack.
Add optional white chocolate drizzle: If using, melt the white chocolate chips with the shortening in a microwave-safe bowl in 15-second intervals, stirring after each interval until smooth. Drizzle over the cooled cookies and let the chocolate set before stacking.