Preheat the slow cooker if necessary; see the manufacturer's instructions. Rinse the salmon in cold water, drain and place in the slow cooker pot. Arrange the carrot, spring onions, mushrooms, chilli and ginger on top of the fish.
Add the miso, soy sauce and mirin (if used) to the hot stock and stir until the miso has dissolved. Pour the stock mixture over the salmon and vegetables. Cover with the lid and cook on low for 1½–2 hours or until the fish is tender and the soup is piping hot.
Lift the fish out with a fish slice and transfer it to a plate. Flake it into chunky pieces, discarding the skin and any bones. Return the fish to the slow cooker pot and add the mangetout. Cook on high for 10 minutes or until the mangetout are just tender, then ladle the soup into bowls and garnish with coriander leaves.