Preheat the oven to 350°F (175°C).
In a bowl, whisk together the flour, baking soda, and salt.
In a separate large bowl, cream together the softened butter, granulated sugar, and powdered sugar until light and fluffy.
Add the egg, vanilla extract, and peppermint extract to the creamed mixture. Mix until well combined.
Gradually add the dry ingredients to the wet ingredients and mix until just combined.
Scoop tablespoon-sized portions of dough onto baking sheets lined with parchment paper, spacing them about 2 inches apart.
Bake in preheated oven for 10-12 minutes, or until the edges are lightly golden.
Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Melt the chopped semisweet chocolate in a heatproof bowl over a pot of simmering water or in the microwave at short intervals.
Dip the cooled cookies halfway into the melted chocolate, allowing any excess to drip off.
Sprinkle crushed peppermint candies over the chocolate coating before it sets.
Let the chocolate set completely before storing or serving.