Preheat oven to 350°F and line two baking sheets with parchment paper and set aside.
In a medium saucepan over low heat, melt the butter and chocolate, stirring together until smooth. Set aside to cool for a few minutes.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a handheld mixer, beat the sugars and eggs together on high speed until pale in color (about 3 minutes).
With the mixer on low speed, slowly add in the chocolate and butter mixture and stir until combined.
Add the flour, cocoa powder, salt, and espresso powder. Mix until well combined.
Using a 1 tablespoon cookie scoop, scoop cookie dough onto prepared baking sheets (about 2 inches apart). Bake for 10 minutes until the cookies are set on the edges but are still slightly gooey in the centers. Cool cookies on the pan on a wire rack.
Melt white chocolate in a small saucepan over low heat, stirring until smooth. Pour melted chocolate into a frosting piping bag and cut a small hole on the end. Drizzle cookies with white chocolate and top with crushed peppermint candies. Enjoy!