Preheat oven to 325 degrees (F). Line two large baking sheets with parchment paper and set aside.
In a medium-sized bowl whisk together the flour, cocoa powder, espresso powder, baking powder, and salt. Set aside.
In a large microwave safe bowl, combine one cup of the chocolate chips and the butter. Heat in the microwave for 20 second intervals, mixing between each time, until butter and chocolate are completely melted and can easily be whisked smooth. Immediately whisk in the vanilla and peppermint extract.
Whisk in both sugars. Beat in the eggs and milk. Add the dry ingredients into the wet ingredients, and stir to combine - be careful not to over mix! Fold in the remaining 1 cup chocolate chips, and gently stir to combine.
Leaving 1 inch between each cookie on the sheet, scoop heaping ⅛ cupfuls of the batter on the prepared baking sheets. Baking one tray at a time, reduce the oven temperature to 300 degrees right after you place them in the oven.
Bake for 16 to 19 minutes, or until the edges are set and the tops are dark and shiny. Allow to cool for a few minutes, and press the white chocolate and dark chocolate chunks on top. Sprinkle with crushed candy canes. Allow to cool on a cooling rack for 15 minutes, then enjoy!