Pre heat the oven to 140/120C fan.
Add the oil to a large frying pan over a medium heat. Add the onions, reduce the heat to low and cook for 40 minutes, turning frequently. Add as splash of water if they start to catch. Stir in the brown sugar and chestnuts and cook for 5 minutes.
Slice the aubergine lengthways to form 1/2 inch slices. Mix the breadcrumbs, parmesan and chill powder. Dip the aubergine slices in the breadcrumb mixture, then coat in the egg and finally coat in the flour. Cook for 2-3 minutes on each side. Place on a baking tray and pop in the oven to keep warm. Repeat the above for the second batch of slices.
Add the potatoes to a large pan of boiling salted water. Boil for 15 minutes or until tender. Drain and leave to steam dry for 3 minutes. Return to the pot and mash well.
Meanwhile add the milk, butter and garlic to a saucepan over a low heat. Once the butter has melted, pour over the potatoes and add the miso paste. Mash well to combine.
Serve the schnitzel, miso mash and caramelised onions with a scattering of fresh parsley.