Boil a large kettle of water. Break the carcass into a big non-stick pan and add the ginger slices, onion and two-thirds of the garlic. Cook, stirring, for about 2 mins – the meat will stick to the base of the pan, but this will add to the flavour. Pour in 1.5 litres of boiling water, stir in the vinegar, then cover and simmer for 2 hrs.
Put a large sieve over a bowl and pour through the contents of the pan. Measure the liquid in the bowl – you want around 450ml. If you have too much, return to the pan and boil with the lid off to reduce it. Transfer the onion from the sieve to a bowl with three-quarters of the sweetcorn. Blitz until smooth with a hand blender.
Return the broth to the pan, and tip in the puréed corn, remaining sweetcorn and garlic, the grated ginger, the whites of the spring onions and the chicken. Simmer for 5 mins, then stir in the tamari. Turn off the heat, and quickly drizzle in the egg, stirring a little to create egg threads. Season with pepper, then ladle into the bowls. Top with the spring onion greens and a few drops of sesame oil, if using.