Turning on the TV in Los Angeles in 1949, you might have come face-to-face with a young man in a jeweled turban with a dreamy gaze accentuated by dark eye shadow. Dressed in a fashionable coat and tie, Korla Pandit played the piano and the organ—sometimes both at once—creating music that was both familiar and exotic.

According to press releases from the time, Pandit was born in New Delhi, India, the son of a Brahmin government worker and a French …