Pour some simple syrup into a shallow dish. Pour the crushed candy cane onto another shallow dish. Dip the rim of your martini glasses into the simple syrup and then the candy cane.
Fill a cocktail shaker halfway with ice. Add 4 ounces whipped cream vodka, 2 ounces white chocolate liqueur, and 2 ounces peppermint schnapps. Shake vigorously for 30 seconds.
Add the half-and-half to the cocktail shaker, and shake to combine.
Divide the cocktail between the two martini glasses, garnish with a mini candy cane and serve.