Heat olive oil in a casserole and seal the chicken for 4 minutes per side.
Add chopped carrots, one lemongrass stalk, three thyme sprigs, and half the coriander stalks to the pan.
Move chicken and vegetables to a deep saucepan and cover with 2 liters of cold water.
Add quartered carrots, two bruised lemongrass stalks, remaining thyme, and remaining coriander stalks to the pot.
Bring to a boil, skim the foam, then simmer covered on low for 90 minutes.
Remove and cool the chicken, then strain the broth and reserve the carrots.
Simmer the strained broth uncovered for 15 minutes to reduce it by one third.
Finely chop the reserved carrots and place them into soup bowls.
Tear the chicken meat into pieces and add to the bowls with salt, pepper, and coriander leaves.
Top with lime zest, extra virgin olive oil, and sliced raw lemongrass.
Ladle the hot broth into each bowl and serve.