No person shall sell, advertise or offer or expose for sale any frozen dessert or frozen dessert mix unless the manufacturer thereof is a licensee under the provisions of section 21a-53. No person shall sell, offer for sale or advertise for sale any frozen dessert or frozen dessert mix if the brand name of the frozen dessert or frozen dessert mix or the label upon it or the advertising accompanying it gives a false indication of the origin, character, composition or place of manufacture, or is otherwise false or misleading in any particular.