Heat grill to high (450° to 550°).
Purée 2/3 cup basil leaves, 1 can coconut milk, and the curry paste in a blender. Cook mixture in a saucepan over medium-high heat, stirring, until bubbly, 2 to 3 minutes. Add remaining can coconut milk, 1/2 cup water, the fish sauce, and sugar. Cook sauce at a low boil until thickened, 10 minutes.
Coat fish with 3 to 4 tbsp. sauce. Coat peppers with about 2 tbsp. sauce.
Oil cooking grate, using tongs and a wad of oiled paper towels. Grill peppers, covered, turning once, until browned, 4 to 5 minutes. Transfer to a plate. Grill fish, covered, turning once, until just cooked through, 3 to 5 minutes. With a wide spatula, carefully transfer to another plate.
Spoon rice onto a large platter and top with fish. Thinly slice remaining basil. Spoon half of sauce over fish, top with peppers, and sprinkle with basil. Serve with lime wedges and more sauce.
Note: Nutritional analysis is per serving.