Cut eggplants into quarters lengthwise, to make thick batons.
Line a large steamer basket with cabbage leaves and lay eggplant slices on the cabbage in a single layer. Cover with lid and steam over boiling water for 15 minutes, or until eggplant has wilted and is tender. Discard cabbage leaves when eggplant is cooked. Remove and discard skin from eggplant.