In a large bowl, combine the first eight ingredients; beat until smooth. Set aside.
Place grated chocolate and additional chocolate syrup in separate shallow bowls. Hold each glass upside down and dip rim in chocolate syrup, then dip in grated chocolate. Pour drink mixture into prepared glasses. Serve immediately.
Editor’s Note: This recipe was tested with commercially prepared eggnog. Melted ice cream should not be stored in the refrigerator, so discard any leftover mixture.