Preheat the oven to 350 F. In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, combine butter with sugar until fluffy.
Add in egg and peppermint extract, and mix until it is smooth. Add in the flour mixture, and mix until all of the flour is combined. Fold in the crushed candy canes.
Roll the cookie dough into balls, and place them at least 2-inches apart onto an ungreased baking sheet. Bake for 10-12 minutes.