Preheat your oven to 325°F (163°C). Line two large baking sheets with parchment paper and lightly spray with non-stick spray to prevent the cookies from sticking. Set these aside for later use.
In a medium-sized bowl, whisk together the all-purpose flour, unsweetened cocoa powder, espresso powder, baking powder, and salt. Once thoroughly combined, set the bowl aside for use after the wet ingredients are ready.
In a large microwave-safe bowl, combine 1 cup of semi-sweet chocolate chips and the room temperature unsalted butter. Microwave on low power in 15-second increments, stirring in between, until fully melted and smooth. Whisk in the vanilla extract and peppermint extract, followed by the granulated sugar and light brown sugar until well combined.
Beat the eggs into the wet mixture one at a time, ensuring each egg is fully incorporated before adding the next. Then, beat in the milk. The mixture will become glossy and thick.
Add the dry ingredients from Step 2 to the wet mixture from Step 4. Gently stir until just combined—take care not to overmix, as this can make the cookies tough. Fold in the remaining 1 cup of semi-sweet chocolate chips, stirring until just incorporated. I find that folding helps keep the batter tender and creates pockets of chocolate in every bite.
Using a 1/4 cup measure, scoop batter onto the prepared baking sheets, leaving 1-inch between cookies. Bake one tray at a time: slide a tray into the oven and immediately reduce the oven temperature to 300°F (149°C). Bake for 16 to 19 minutes, or until the edges are set and the tops appear dark and shiny. If the cookies spread too much, use a spatula to gently press the edges inward while they're still warm.
While the cookies are still warm out of the oven, gently press a few white chocolate chunks and dark chocolate chunks into the tops. Sprinkle the crushed candy canes over the cookies for a festive look and minty flavor. Allow the cookies to cool completely on the baking sheet before serving. For an extra pop of color and crunch, I like to reserve a bit of the crushed candy canes to sprinkle just before serving.