Preheat oven to 350 degrees. Prepare baking sheets with silicone liners or parchment paper or by using cooking spray.
In a medium mixing bowl whisk together flour, cocoa powder, baking soda and salt and set aside.
In the bowl of an electric stand mixer fitted with the paddle attachment mix together butter, granulated sugar and brown sugar until well combined.
Mix in one egg at a time then blend in milk, vanilla extract and peppermint extract.
With mixer set on low speed slowly add in flour mixture and mix just until combined.
Scoop dough out by a rounded tablespoon and place on cookie sheets about 1-2 inches apart.
Bake in preheated oven about 8 minutes (cookies should appear slightly under-baked). They will be soft and a little chewy.
Let cool on baking sheet several minutes then transfer to a wire rack or plate to cool.
Once cookies are completely cool, melt white chocolate in a microwave safe bowl per package instructions.
Dip half of each cookie in white chocolate or drizzle with white chocolate then transfer to parchment paper and sprinkle with peppermint bits. Chill to let chocolate set about 10 minutes or more.
Enjoy with a cold glass of Florida milk.
Store leftover cookies in an airtight container or, better yet, share them with friends and family!