1Cook shallot in 2 tablespoons oil in a 12-inch nonstick skillet over moderate heat, stirring occasionally, until golden, 3 to 5 minutes.
2Add chile and cook, stirring, until softened, about 1 minute.
3Add mangoes, fish sauce, sugar, and salt and cook, stirring occasionally, until mango is softened and mixture is slightly thickened, 3 to 7 minutes.
4Remove from heat and stir in lime juice. Transfer relish to a bowl.
5Pat fish dry and season with salt and pepper.
6Heat remaining tablespoon oil in cleaned skillet over moderately high heat until it just begins to smoke, then cook fish, skin side down first, turning over once, until golden and just cooked through, 12 to 16 minutes total.