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1
Place the wok over medium-high heat and add the thick top layer of the coconut milk — the cream — to the dry wok, so the fat renders out without the thinner milk diluting it and slowing the process. Fry, stirring continuously, until the cream separates and the oil rises visibly to the surface. The cracking is complete when the cream looks oily and glossy, not wet.
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2
Add the green curry paste to the cracked coconut cream and fry, pressing and folding the paste through the fat, so the heat of the oil drives off the raw, sharp edge of the lemongrass, galangal, and shrimp paste and replaces it with a deep, toasted fragrance. Keep moving the paste — it will catch and scorch quickly at this stage. The paste is ready when it has darkened slightly and no longer smells sharp.
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3
Pour in the remaining coconut milk and bring to a gentle simmer, then add the kaffir lime leaves. This is where the dish lives or dies: season the curry base thoroughly with fish sauce and palm sugar now, before the fish enters the wok, because any adjustment once the fish is in the sauce requires the kind of stirring that will break the flesh. Taste — the sauce should read balanced across salt, sweetness, and heat.
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4
Add the fish medallions or bone-in steaks to the simmering curry and do not stir; instead, use a spoon to baste the sauce over the fish so the flesh cooks evenly from above and below without being disturbed. Cook for 4–5 minutes only, then remove the wok from heat while the thickest part still shows a trace of pink, so the carryover heat finishes the cooking gently and the flesh stays cohesive rather than tightening and flaking apart. The flesh should yield to gentle pressure at the surface but remain cohesive.
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5
Scatter Thai basil leaves and sliced green chillies over the surface. Serve immediately — the curry sauce should be slightly thinner than a chicken green curry, as the fish will have released its juices into the sauce during cooking.