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. Meanwhile, in a medium saucepan, bring the carrots, garlic, and broth to a boil. Cook, covered, over moderately low heat until the carrots are tender, about 15 minutes. Puree the carrots, garlic, and broth in a blender and pour back into the pan. Add the milk, fish sauce, curry paste, brown sugar, and 1/2 teaspoon of the salt and bring to a simmer, stirring occasionally.
3. In a large nonstick frying pan, heat the oil over moderately high heat. Season the fish with the remaining 1/4 teaspoon salt. Cook the fish, skin-side down, until golden, about 4 minutes. Turn, reduce the heat to moderate, and continue cooking until just done, about 4 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: Very few wines mesh as well with Asian spiciness as riesling; it's the clear choice here. Go for an off-dry one from Washington State.
Notes: Asian fish sauce and red Thai curry paste are available at Asian markets and many supermarkets