• Preheat the oven to 350°F (175°C).
• Beat butter and 3/4 cup powdered sugar until fluffy. Add vanilla, peppermint extract, and egg, beating until well combined.
  
• In a separate bowl, whisk together flour, baking powder, and salt.
  
• Gradually add dry ingredients to the butter mixture, beating until well combined. Stir in 1/2 cup crushed candy canes by hand.
  
• Form dough into small balls using about a teaspoon of dough. Roll these in granulated sugar to coat, and place on a baking sheet lined with parchment paper.
  
• Bake for 10-12 minutes until they are just set but not browning.
• Let cookies cool on the baking sheet for a few minutes, then transfer to a wire rack.

Make the glaze:

• Mix the remaining 3/4 cup powdered sugar with milk to create a thick but pourable glaze.
  
• Drizzle glaze over cooled cookies and sprinkle immediately with the remaining crushed candy canes.