Combine crushed candy canes and granulated sugar in a small bowl and mix well to combine. If desired, rim the top of each glass with candy cane and sugar mixture and fill with ice.

Fill a cocktail shaker with Peppermint Schnapps, Kahlúa, vodka and ice. Shake well until combined and cold. Pour into prepared glass and top with desired amount of half-and-half or whole milk.

Garnish with additional candy canes, if desired.