Dissolve the miso and sugar in 50ml/2fl oz of water in a saucepan, then bring the mixture to the boil. Reduce the heat and simmer for 8-10 minutes, or until it has thickened and darkened in colour. Decant the mixture into an airtight container such as a squeezy bottle fitted with a small nozzle lid (it can be kept like this in the fridge for 1 week).
Heat the oil in a deep-fat fryer to 180C. Alternatively, heat the oil in a deep, heavy-based frying pan until a breadcrumb sizzles and turns brown when dropped into it. (Caution: hot oil can be dangerous. Do not leave unattended.)
Deep-fry the diced aubergine, in batches if necessary, for 2-3 minutes, or until golden-brown and crisp. Remove from the oil using a slotted spoon, then set aside to drain on kitchen paper. Sprinkle over the chopped coriander and mix together. Repeat the process with the remaining aubergine.
Heat the butter in a large frying pan over a medium to high heat. When the butter is foaming, add the halibut pieces (in batches if necessary) and fry on each side for 2-3 minutes, or until golden-brown and just cooked through. Add the edamame beans and continue to fry until warmed through.
Mix the sesame seeds together.
To serve, spoon the fried aubergines onto the serving plates, scatter over the edamame beans, then sprinkle the sesame seeds on top. Finish with 2 pieces of fish and a drizzle of the miso sauce, then garnish with the mixed cress.