01 - Preheat oven to 350°F and line two baking sheets with parchment paper.
02 - Combine flour, baking soda, baking powder, and salt in a medium bowl and whisk until thoroughly blended. Set aside.
03 - In a large bowl, beat unsalted butter, granulated sugar, and light brown sugar using an electric mixer or hand whisk until light and fluffy, about 2–3 minutes.
04 - Incorporate the egg, whole milk, peppermint extract, and vanilla extract into the butter-sugar mixture, mixing until fully combined.
05 - Gradually add the dry ingredients to the wet mixture, stirring gently until the dough just comes together without overmixing.
06 - Portion dough into tablespoon-sized balls and arrange on prepared baking sheets, ensuring 2 inches between each.
07 - Place baking sheets in preheated oven and bake for 9–11 minutes until edges set but centers remain soft. Watch carefully to avoid overbaking.
08 - Remove cookies from oven and allow to cool on baking sheets for 5 minutes before transferring to a wire rack to cool completely.
09 - Whisk powdered sugar, lemon-lime soda, and peppermint extract together in a bowl until smooth.
10 - Drizzle glaze evenly over cooled cookies, then immediately sprinkle with crushed peppermint candies. Let glaze set for at least 15 minutes before serving.