How to Make It
Rinse the rice until the water runs clear. Put the rice in a small saucepan with the water. Bring to a boil, reduce the heat to low, and cook, covered, for 15 minutes. Remove the pan from the heat and let sit, without removing the lid, for 10 minutes.
In a medium saucepan, heat the thick coconut milk from the top of the can over moderate heat. Add the curry paste and cook, stirring, for 3 minutes. Whisk in the remaining coconut milk, the broth, fish sauce, brown sugar, turmeric, and 1/4 teaspoon of the salt and bring to a simmer. Cook, stirring frequently, until slightly thickened, about 7 minutes.
In a shallow bowl, combine the flour, the remaining 1/2 teaspoon salt, and the pepper. Coat the fish with the flour mixture and shake off any excess. In a large nonstick frying pan, heat the oil over moderately high heat. Put the fish in the pan, skinned-side down, and cook until golden, about 3 minutes. Turn and continue cooking until just done, about 2 minutes longer for 1-inch-thick fillets. Mound the rice on plates and top with the fish and the sauce. Sprinkle with the cilantro, if using, and serve with the lime wedges.
Thai curry paste and Asian fish sauce are available at Asian markets and many supermarkets.