In a blender, combine the cilantro, scallions, oil, ginger, lime zest and juice and ¼ teaspoon each salt and pepper. Blend on high until smooth, about 1 minute, scraping the jar as needed. Measure ¼ cup of the puree into a wide, shallow dish; transfer the remainder to a small bowl and reserve. Add the fish to the dish, rub the puree into all sides and season with salt.
Heat a 12-inch grill pan over high until water flicked onto the surface immediately sizzles and evaporates. Using a heat safe brush, lightly brush the pan with oil, then place the fillets flesh side down in the pan. Cook until the fish releases easily, 2 to 3 minutes. Using a thin metal spatula, flip the fillets and cook, turning as needed, until the flesh flakes easily, 4 to 6 minutes. Serve with the reserved puree and lime wedges.
Optional garnish: Thinly sliced Fresno OR serrano chilies
