Peel the prawns, setting the shells to one side. Return the prawns to the fridge. Peel half the shallots then roughly chop them. Warm half the oil in a deep pan then add the shallots and fry them until they are soft and pale gold.
Split the stalks of lemongrass lengthways, discarding the tough, outer leaves, then bash them hard with a heavy weight, such as a rolling pin, to splinter them. Add the shattered stalks to the shallots.
Peel the ginger, cut it into coins about as thick as a £2 piece, and add them to the shallots. Continue cooking over a low heat.Add the reserved prawn shells to the pot. Pour the water into the pan and bring to the boil. Lower the heat, then leave to simmer for 30 minutes.
Peel the remaining shallots, cut them in half, then open into individual layers. Peel the carrots, cut into thin slices then into short matchsticks. Warm the remaining groundnut oil in a large pan, then cook the shallots until golden.
Cut the sugar snap peas into thin strips. Add the reserved prawns and cook them for 3 minutes on each side. Strain the broth through a sieve into the shallots and prawns.
Add the carrots and sugar snaps and season with the fish sauce, then cook for a minute or two before tearing the coriander leaves and adding them to the soup. Serve immediately.