1. Devein the prawns, remove the heads and shells (don't throw these away) and keep the tails. Heat the oil in a saucepan and stir-fry the heads and shells until the flavours start to develop. Add the stock and lime or lemon leaves and allow to simmer for 15 minutes.
2. Heat the butter in a separate saucepan and fry the mushrooms until soft. Add the ginger, lemon grass and spring onions, as well as the Tom Yum paste. Pour the stock through a sieve and add to the mushrooms in the saucepan. Bring the mixture to the boil.
3. Fry the prawns in hot butter in a frying pan and season with salt and freshly ground black pepper. Transfer the prawns to the soup.
4. Add the coconut milk, coriander, fish sauce, lime or lemon juice and brown sugar. Allow to simmer for a few minutes so that the flavours can develop.
5. Cook the noodles according to the directions on the package and divide them among four serving bowls. Ladle the soup over the noodles, garnish with fresh coriander and serve.