See fungee. Sense 2 (“style of folk and popular music”) is apparently from the fact that the music is a blend of different musical instruments and styles, just as the dish (sense 1) is a blend of different flavours.
Meanings
(alt-of, alternative, uncountable) Alternative spelling of fungee (“a cornmeal dish from the Caribbean, usually made with okra and served with salt fish, shellfish, or chicken”).
(broadly, uncountable) A style of folk and popular music from the Virgin Islands, traditionally performed by bands consisting of banjo, guitar, ukulele, and washboard with various percussion instruments on rhythm.