To add a crushed candy cane rim to the glass, melt some mini chocolate chips in the microwave in 10-second bursts, stirring in between, until they are melted and smooth.
Place the crushed candy canes into a shallow dish.
Dip the rim of a glass into the melted chocolate, then dip the glass into the crushed candy canes.
Place the glass in the refrigerator for the chocolate to set while mixing the cocktail.
For the cocktail, pour the milk, peppermint schnapps, white chocolate liqueur, vodka, and peppermint mocha creamer (if using) into a cocktail shaker filled with ice.
Shake for 15-30 seconds to combine well.
Strain the cocktail into the rimmed glass.
Garnish with a mini candy cane. Serve and enjoy!