Rim the glass with candy cane (optional): Place 1 or 2 candy canes in a plastic bag and use a rolling pin to bust them up into small pieces. Transfer the crushed candy canes to a plate and set them aside. Next, combine the 2 tablespoons of sugar and 1 tablespoon of water in a small bowl until the sugar is completely dissolved. If you need to you can heat this up in the microwave for 15 to 20 seconds to help the sugar dissolve. And finally, dip the rim of a lowball glass into the sugar solution, followed by a dip in the crushed candy canes so that they adhere to the rim.
Make the drink: Pour the peppermint schnapps/creme de menth, vodka, and Kahlua into your lowball glass. Fill the glass with ice cubes and top it off with either milk, half & half, or heavy cream. Stir these ingredients with a candy cane until combined.
Serve the peppermint white russian immediately and enjoy!