Add the candy canes in a large zip bag and seal. Place the bag onto a flat, sturdy surface such as a heavy-duty cutting board. Use a meat mallet or rolling pin to crush the candy canes into fine pieces.
Place the crushed candy cane in a small bowl or plate.
Place the chocolate chips in a microwave-safe bowl that is large enough to fit the rim of your serving glass. Microwave, pausing every 15 seconds to stir the chocolate until it's melted and smooth.
Slowly dip each serving glass into the melted chocolate and allow excess chocolate to drip off. After a couple of seconds, dip the white chocolate-covered rim into the crushed candy canes.
Place the glasses upright in the refrigerator for 20 minutes to allow the chocolate and candy to harden.
Make the milkshake:
In a blender, combine the peppermint ice cream and milk. Blend for 15-20 seconds until it reaches a thick, milkshake consistency.
Serve:
Pour the milkshake into the candy cane rimmed glasses. Top with whipped cream and sprinkle with crushed candy canes. Serve immediately.
Notes
To make this milkshake without peppermint ice cream, blend 2 cups of vanilla ice cream with ½ cup milk and ½ teaspoon peppermint extract.
For a dairy-free milkshake, use your favorite dairy-free vanilla ice cream, ½ teaspoon peppermint extract, and ½ cup non-dairy milk such as almond or soy. Place all of the ingredients in the blender and blend until smooth. Skip the white chocolate rimmed glasses and serve this milkshake topped with whipped coconut cream and crushed candy cane.