Golden Eggplant is an unusual treasure item that can be only be found during your first expedition. Like other treasures, it be found inside shrines or tombs, or as buried treasure. It can be traded during expedition (though its Value is only 40 when trading with natives), or saved to exchange for Fame or Funds upon return to London.
Note that there are normally no tombs in the land that you visit during your first expedition, except if you play as Freya Stark and take advantage of her Desert Explorer perk in order to explore a Desert biome.
Unlike other treasures, the Golden Eggplant is worth a considerable amount of karma at an altar and donating it there unlocks the hidden achievement 'A tribute to Yama'.