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1
Sauté the prawn shells and heads briefly in a little oil over high heat until they turn pink and fragrant, so the dry heat draws colour and roasted depth from the shells before the water ever touches them. Add 1 litre of water and simmer for 20 minutes, then strain. The stock is ready when it tastes clearly of prawn — the aromatics will intensify a good stock, but they cannot create one from nothing.
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2
Bring the prawn stock to a gentle simmer in a wide saucepan and add the bruised lemongrass, sliced galangal, and torn kaffir lime leaves, bruising and tearing them so their volatile oils bleed into the broth rather than staying locked inside. Simmer for 2–3 minutes. After 2 minutes, test by smell: the broth must carry an intense, citrus-green character of lemongrass and kaffir lime — a faint smell tells you the lemongrass was not bruised hard enough.
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3
Add the fish sauce and palm sugar, stirring until the sugar has dissolved so it integrates evenly rather than sitting in a sweet patch at the bottom. Add the split chillies, splitting them so the seeds are exposed to the broth and the heat builds fully. The broth now carries its complete seasoning base.
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4
Add the prawns and cook in the hot broth for 60–90 seconds only, watching the shape rather than the clock — the prawn is done when it has turned fully opaque and curled into a 'C', not a tight 'O', which tells you it has gone a breath too far. Remove the pan from the heat the instant the prawns reach this point, since they will continue to cook in the residual heat of the broth.
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5
This is where the dish lives or dies. With the pan entirely off the heat, add the lime juice immediately before serving, so the volatile aromatic oils that give tom yam its vivid citrus lift are not driven off by heat — the acid survives, but the freshness does not, and a soup finished over heat or left to rest after the lime goes in will taste merely sour rather than sour and alive. Taste at once: the dominant note must be sour, the secondary hot, the third savoury; adjust with more fish sauce for salt, more lime for sour, or a pinch of palm sugar if the acidity is too sharp, then stir in the nam prik pao and add the mushrooms.
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6
Ladle immediately into warmed bowls, leaving the lemongrass and galangal pieces in the soup so they continue to release aroma into the hot liquid at the table — they are moved aside when eating, not removed before service. Scatter coriander leaf over each bowl and serve at once.