Crush the chocolate wafer cookies into fine crumbs about 1/8-inch in size—you want them small enough to coat evenly but still have some texture. Crush the candy canes into small shards about 1/4-inch pieces; I recommend placing them in a sealed bag and using a mallet or rolling pin to break them down, which keeps the pieces contained and prevents a sticky mess on your counter. Chop the white chocolate into small, uniform pieces to ensure it melts evenly and smoothly. Have all ingredients measured and ready before you begin melting.
Melt the chopped white chocolate using a double boiler or microwave in 30-second intervals, stirring between each interval to prevent overheating and seizing. Once completely smooth and melted, stir in the peppermint extract until fully combined. The mixture should be warm enough to dip but not so hot that it's thin and runny—if it's too thick, let it cool for a minute or two before proceeding.
Working quickly while the chocolate is still pliable, dip each chocolate wafer cookie into the peppermint-white chocolate mixture, using a fork or dipping tool to ensure it's fully coated but excess drips off. Place each dipped cookie on a wire rack or parchment paper. I like to work in batches of 5-6 cookies at a time so the chocolate doesn't cool too much before you finish dipping.
While the white chocolate coating is still soft and tacky, immediately sprinkle the crushed candy cane shards generously over the top of each dipped cookie. The warmth of the chocolate will help the candy adhere. Allow the cookies to cool completely at room temperature until the chocolate is fully hardened, about 30-45 minutes, or refrigerate for faster setting.