Using a superfine grater, grate bittersweet chocolate onto a saucer. Use a finger to rub 1/3 teaspoon corn syrup around rims of each of 6 glasses. Roll each rim in the grated chocolate and set aside. Pour crème de menthe, white-chocolate liqueur, and vanilla-infused vodka into a shaker filled with ice. Shake until well blended. Strain into glasses (be careful not to splash off the chocolate rims). Serve each cocktail with a sprig of mint.