1. 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.
2. 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.
3. 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.
Wine Recommendation: The perfumed heat of this dish with its full-bodied coconut sauce makes a cold beer a great companion. If you prefer wine, experiment with a moderately priced sparkling one from California.
Notes: Thai curry paste and Asian fish sauce are available at Asian markets and many supermarkets