1. Preheat the oven to 400 degrees. Heat a large skillet over medium-high heat. Spoon a few tablespoons of the coconut "cream" (the thick part from the top of the milk) into the pan. Add the curry paste and cook, stirring, 2 minutes. Stir in remaining coconut milk and the brown sugar; bring to a boil. Reduce heat to medium and simmer, 6 to 8 minutes.
2. Heat a large nonstick oven-safe skillet over medium-high heat. Season the salmon with the black pepper and 1/4 teaspoon of the salt. When the pan is very hot, add the oil. Add the salmon; cook 2 minutes to sear, and turn over. Transfer skillet to oven; roast salmon until barely cooked through, about 5 minutes.
3. Stir the lime juice and remaining salt into the sauce. Spoon 2 tablespoons sauce over each piece of fish and serve with rice. Garnish with lime wedges and serve with additional sauce if desired.