Preheat the oven to 200C/180C Fan/Gas 5. Heat a deep-fat fryer to 180C. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
For the duck, heat a large frying pan and add the oil. Once hot, add the duck breasts and cook skin-side down for 3-4 minutes. Turn the duck over and place in the oven for 6-8 minutes, depending on the size of the duck breast, until cooked through.
Remove the duck from the oven and, using a large meat fork, hold one breast over the deep-fat fryer. Using a ladle, pour the hot oil over the duck skin for 1-2 minutes, or until golden-brown and crisp. (CAUTION: hot oil can be dangerous. Take care when ladling the oil over the duck.) Set aside, covered with aluminum foil, to rest. Repeat with the remaining duck breasts.
Heat a deep-fat fryer to 180C. Deep-fry the aubergine for 2-3 minutes or until golden-brown and crisp. Set aside to drain on kitchen paper.
Add the white miso, sugar, honey and 100ml/3½fl oz water to a saucepan. Over a medium heat, cook until it has reduced in volume and turned golden-brown.
To serve, bring a pan of salted water to the boil and blanch the kale for 1-2 minutes. Drain and place on serving plates. Slice the rested duck breasts. Place the aubergine on the plates and spoon over the sauce. Arrange the duck around the plates and garnish with the edamame beans, sesame seeds and micro cress.