Preheat oven to 350 F. Line a cookie sheet with parchment paper.

Beat butter, sugar, milk and peppermint extract together in a bowl. Sift flour into the butter mixture and stir to fully combine the ingredients. Use your hands to pack the dough into a ball and wrap in wax paper or plastic wrap. Refrigerate for 20 minutes.

Place chilled dough on a floured work surface and roll out to a half-inch thickness. Use a cookie cutter or knife to cut the dough into your desired shape and transfer to the prepared cookie sheet.

Bake the cookies for 10 to 11 minutes, watching the color closely until they just start to turn a light golden color. Remove cookies from the oven and let rest for 2 to 3 minutes before transferring to a wire cooling rack to cool completely. (Save your parchment-lined cookie sheet.)

Melt chocolate over a double broiler until smooth and silky. Dip the cooled cookies in the chocolate and sprinkle crushed peppermint candies on the chocolate while it’s still wet. Place on your previously used parchment-lined cookie sheet to cool and set before serving.

Serve with a glass of warm vanilla milk rimmed in crushed peppermint candies: Lightly dampen the edge of a glass and roll in the crushed peppermint candies, pressing slightly to adhere them to the glass. Add vanilla extract to milk and heat, stirring occasionally, over medium-low on the stovetop or in a microwave in 30-second bursts (or steam it if you have a steamer/espresso machine). Adjust vanilla to taste, then fill prepared glass with milk and serve.