Preheat the oven to 350°F. Line baking sheets with parchment paper.
Whisk together the flour, cocoa powder, baking soda, baking powder, and salt.
Cream the softened butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the eggs, then add the vanilla extract and milk.
Add the dry ingredients and mix just until a soft dough forms. It might take a minute for the dough to come together, but it will.
Scoop the dough into tablespoon-sized portions and roll into balls. Place on the prepared baking sheets, spacing the cookies about 2 inches apart.
Press an indentation into the center of each dough ball using your thumb or the back of a teaspoon.Tip: Dip the back of the teaspoon in baking cocoa to prevent it from sticking to the cookie dough.
Bake for 7–8 minutes. Gently re-press the centers while the cookies are still warm.
Cool the cookies completely.
Place the Andes Peppermint Crunch candies in a microwave-safe bowl. Microwave in short intervals, stirring every 15–20 seconds, until melted and smooth.
Spoon the melted peppermint candy into the center of each cookie.
Chop the reserved candies and sprinkle over the filling. Let the filling set before serving.
Video
Notes
For a softer filling, add 3-4 Tbsp. heavy cream to the unmelted candies before microwaving. Heat and stir in short intervals until smooth. Allow the ganache to sit for a few minutes before spooning it into baked cookies.