Add corn syrup to a small dish and the crushed candy canes to a second small dish.
Dip the rim of your serving glass into the corn syrup, and rotate the glass so the entire rim is coated in the syrup.
Hold the glass above the syrup dish and wait about 30 to 60 seconds for any excess syrup to drip off. You can twirl the glass in your hand if you need to to make the coating more even.
Dip the syrup-coated rim into the candy cane pieces. Give it a second or two before lifting the glass out of the candy, then turning the glass slightly and dipping again. Repeat until the entire rim is coated.
Set the glass aside while you make the drink.
Cocktail
Measure and add the vanilla vodka, peppermint schnapps, white chocolate liqueur, and half and half to a cocktail shaker.
Fill the shaker with ice, seal it and shake for 15 to 20 seconds.
Open the shaker and use a cocktail strainer to strain the drink into your prepared glass.
Add the whole candy cane to the side of the glass as an extra garnish, and serve.