Cook the chestnuts in simmering water for about 45 minutes, or until tender, then drain. Blanch the cabbage in boiling water for 2 minutes, then refresh in iced water and drain on paper towel.
Heat the oil in a wok or deep-fryer until just smoking (180°C/350°F), and deep-fry the cabbage in two batches until golden. Remove with a slotted spoon and drain on paper towel. D