Shiitake Mushroom (Lentinula edodes).  Only the button mushroom is cultivated more than the shiitake, which is prized by cooks and herbalists alike. Shiitake is a forest mushroom native to Japan, China and Korea. The Japanese name — shiitake (shee-tah-ki) is derived from “shii” meaning 'shiia' the oak tree on which they grow and “ta-ke” meaning mushroom.