01 - Preheat oven to 350°F and line two baking sheets with parchment paper.
02 - In a medium bowl, whisk together all-purpose flour, baking soda, baking powder, and salt.
03 - Cream the softened unsalted butter with granulated sugar and light brown sugar until light and fluffy, about 2 to 3 minutes using an electric mixer.
04 - Beat in the egg, whole milk, peppermint extract, and vanilla extract until fully combined.
05 - Gradually integrate the dry ingredients into the wet mixture, blending only until just incorporated.
06 - Scoop tablespoon-sized balls of dough onto the prepared baking sheets, spacing each ball 2 inches apart.
07 - Bake the cookies for 9 to 11 minutes until the edges are set but the centers remain soft. Avoid overbaking.
08 - Allow cookies to cool on the baking sheets for 5 minutes, then transfer to a wire rack to cool completely.
09 - Whisk together the sifted powdered sugar, lemon-lime soda, and peppermint extract until smooth.
10 - Drizzle the glaze over cooled cookies and immediately sprinkle with crushed peppermint candies. Let the glaze set for at least 15 minutes before serving.