Preheat oven to 350°F (175°C) and line two large baking sheets with parchment paper.
In a stand mixer fitted with the paddle attachment, cream the softened butter, granulated sugar, and brown sugar on medium-high speed for 3 minutes until light and fluffy.
Add the egg, vanilla extract, and peppermint extract, beating until fully incorporated.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt.
Reduce mixer speed to low and gradually add the dry ingredients to the wet mixture, mixing only until no flour streaks remain.
Fold in the semi-sweet chocolate chips and 1/4 cup of the crushed peppermint candies by hand.
Scoop 1.5-tablespoon portions of dough and place them on the prepared baking sheets, spaced 2 inches apart.
Bake for 9 to 11 minutes, or until the edges are set and lightly golden but the centers remain soft.
Immediately sprinkle the remaining 1/4 cup of crushed peppermint candies over the tops of the warm cookies.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.