Preheat your oven to 325 degrees Fahrenheit and prepare two large baking sheets by lining them with parchment paper.
In a large bowl with a hand mixer, or in the bowl of your stand mixer, whip the butter on medium high speed for about 2 minutes or until it's light and fluffy.
Add the sifted powdered sugar and mix on low speed together with the butter until incorporated.
Add the egg white and the peppermint extract, and continue to mix on medium low speed until completely incorporated.
Add the flour and salt and mix on low until completely incorporated, scraping down the sides of the bowl.
Add the dough to a piping bag fitted with an open star tip and pipe the cookies onto the baking sheet, starting in the middle and piping in a circular motion outward. Gently smooth out the end after you pipe each cookie with a clean finger.
Bake the cookies at 325 degrees Fahrenheit for about 9-10 minutes, or just until the cookies lose their shine. Remove them from the oven before they begin to brown around the edges.
Let the cookies cool on a wire rack until they're cooled completely.
Melt the white chocolate in a double boiler or in a microwave-safe bowl in the microwave on 50% power for 30 second increments just until it's melted completely.
Stir a few drops of peppermint extract into the melted white chocolate.
Dip each of the cookies into the melted white chocolate about half-way and place them back onto the wire rack or onto a baking sheet lined with parchment paper.
Sprinkle some crushed candy canes or sprinkles onto the white chocolate while it's still wet.
Let the cookies sit until the white chocolate has set (place them in the fridge to set quickly, if desired).
Store in an airtight container for up to 3 days, or serve immediately.