1. Rim glasses Put water into shallow plate or saucer. Put sugar in another plate. Dip rims of four martini glass in water, then dip into sugar. Let dry.
2. Add coffee liqueur, white chocolate liqueur, vodka, cream, peppermint flavor and vanilla extract to a cocktail shaker. Fill with ice. Shake until condensation forms on the shaker.
3. Strain into chilled and rimmed martini glasses. Garnish with peppermint sticks. Serve immediately.