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.
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.
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.
Asian fish sauce and red Thai curry paste are available at Asian markets and many supermarkets