Remove the crown; cut the aubergine into roughly 2 cm thick slices. Score the slices with a knife.
Make a marinade out of the sesame oil, hoisin sauce, rice wine vinegar, Kikkoman soy sauce, a little freshly ground chilli, and the grated ginger.
Brush the marinade onto the purpura slices in a thick layer. Grill the auberigne slices on both sides for about 20 minutes total on a moderately hot BBQ or in a grill pan until they are golden brown, soft, and cooked.