In a large bowl or stand mixer, cream together butter and sugar. Mix in egg, yolk and vanilla. Scrape the bowl as needed. Mix in salt, baking powder and flour. Increase speed and continue mixing until no streaks remain and batter is fully combined. Cover and chill for 30-60 minutes. 

Preheat oven to 350°F. Prepare a baking sheet with a silicone baking mat or parchment paper. 

Scoop dough using a medium cookie scoop. Shape dough into smooth balls and gently flatten to roughly 2 inches wide and between a 1/4 and 1/2 inch in thickness. 

Bake for 10-11 minutes. Allow cookies to rest on the baking pan for 1 minute before transferring to a wire rack to cool completely. 

When cookies have cooled completely, prepare frosting. In a medium bowl, mix together powdered sugar and butter until combined and crumbly. Add peppermint extract and 1 tablespoon of milk or water at a time until desired consistency is reached. 

Frost cookies using a small offset spatula. Immediately sprinkle with crushed peppermint candy canes. Allow frosting to set completely prior to storing in an airtight container.