A steamer accessory includes a water reservoir communicating with the outside via a filling orifice, and a steam generator including a steam production chamber connected to at least one steam distribution outlet provided in a lower part of the steam generator, the water reservoir communicating with the steam production chamber via a water supply inlet. The steam production chamber communicates with at least one steam evacuation outlet disposed higher up than the water supply inlet, the steam production chamber being confined above the steam evacuation outlet(s), the or each steam evacuation outlet communicating via a duct with the or one of the steam distribution outlet(s).