For the base, heat a large flameproof casserole over a medium heat. Add the olive oil and seal the chicken for 3-4 minutes on each side until it just starts to colour. Add the carrots, lemongrass, thyme and half the coriander stalks. Cook for 5 minutes until the chicken has more colour and the vegetables are also coloured slightly.
For the broth, transfer the chicken and vegetables to a large, lidded, deep saucepan and cover with approximately 2 litres/3½ pints cold water. Bring to the boil and skim off any foam. Add the carrots, bruised lemongrass, thyme and the remaining coriander stalks. Turn the heat down to very low, cover and cook for about 1½ hours until the chicken starts to fall from the bone.
Remove the chicken and let it cool. Strain the broth and reserve the vegetables. Return the broth to the heat and simmer for about 10-15 minutes uncovered, until the broth has reduced by one third.
Meanwhile, carefully lift the quartered carrots out of the strainer discarding the rest of the vegetables. Finely chop the carrots and put in deep soup bowls.
When the chicken is cool enough to handle, remove the skin then pull the meat from the bones and tear it up into small pieces. Add the chicken and a pinch of salt and pepper to the bowls, then scatter over the coriander leaves. Sprinkle the lime zest over and drizzle with extra virgin olive oil.
Remove the tough outer leaves, top and root from the remaining lemongrass stalk, then slice very thinly and add to the bowls. By now, the broth should be ready, so simply add a couple of ladleful’s to each bowl before serving.