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You will need a wide-based shallow casserole about 30cm in diameter, or a deep-sided sauté pan, with a tight-fitting lid as the salmon needs to steam in a single layer. Pick the coriander leaves off the stalks, finely chop the stalks and put the leaves in a bowl. Grate the zest of one of the limes. Set aside. Pour both cans of coconut milk into a large jug, then fill one of the empty cans with cold water and stir this into the jug.
Heat the oil and butter in the pan over a lowish heat, tip in the shallots and sizzle gently for about 5 minutes, stirring, until they start to turn golden. Stir the curry paste in and cook for another minute.
Take the pan off the heat and add the lime zest, coriander stalks, rice and a heaped teaspoon of salt, then mix everything together until the rice is coated in the curry paste. (You can prepare this up to two hours ahead.)
Pour the coconut milk mixture over the rice and stir. Bring to simmering point on a medium heat, stirring gently now and then. Get the spoon right to the bottom of the pan so the rice doesn’t stick to it. Scatter in the lime leaves and leave everything to simmer, uncovered, for 5 minutes.
Stir the rice once more, then lay the salmon fillets on top. Cover and leave to barely simmer over a very low heat for 15-20 minutes until the salmon looks cooked and the rice is tender. Cook everything very gently or you will have crunchy rice on the bottom and no liquid left.
While the fish is cooking, juice two of the limes (the grated lime and another) and in a small bowl mix the juice with the soy sauce and sugar until the sugar has dissolved. Trim the spring onions, then split lengthways and slice into thin strands on the diagonal. Mix the spring onions and chilli with the coriander leaves. Cut the third lime into six wedges.
When the rice and fish are ready, take the pan off the heat and leave to stand for 5 minutes. To serve, scatter a third of the coriander salad over everything in the pan. Spoon some coconut rice on each plate, then, using a fish slice, put a salmon portion on top. Drizzle with some of the soy and lime dressing and scatter a spoonful of the coriander salad on top. Give everyone a lime wedge to squeeze over it. Serve the remaining dressing if anyone wants extra, and a side salad.