Preheat the oven to 350°F (180°C). Line two baking sheets with parchment paper, then set them aside.
Place the butter and chopped chocolate in a heatproof bowl and set over a pan of gently simmering water to create a double boiler. Stir occasionally until the chocolate is fully melted. Then remove the bowl from the heat and set it aside.
In the bowl of a stand mixer fitted with the whisk attachment or in a large bowl using an electric hand mixer, whisk together the granulated sugar, dark brown sugar, eggs, vanilla extract, and peppermint extract for 5-6 minutes on medium-high speed; the mixture should resemble an extremely thick, pale yellow pancake batter.
With the mixer on, pour in the slightly cooled chocolate mixture and mix until smooth, about 2 minutes. Sift in the flour, cocoa powder, espresso powder, and salt, and use a rubber spatula to gently fold until just combined.
Using a large (3-tablespoon) spring-loaded cookie scoop, drop 6 cookies on each prepared pan. Make sure to leave plenty of space between each cookie as they will spread when they bake.
Bake for 12-13 minutes. The cookies will be soft so allow them to cool on the baking trays for at least 10 minutes before carefully removing to a wire rack to cool completely. Once the cookies are cool, place the peppermint cream cheese frosting in a piping bag fitted with an open star tip (Wilton 1M). Frost with each cookie, then sprinkle with crushed peppermint candy. Cover and store leftover cookies in an airtight container in the fridge for up to 3 days.