In a large cast-iron or other heavy skillet, heat 1/4 inch oil over high until shimmering. (Test by dropping a breadcrumb; if it sizzles and floats instantly, the oil is hot enough for frying.) Working in batches so as not to crowd, dredge fish in breadcrumbs and lay flat in skillet. Reduce heat to medium and cook until fish are golden brown on bottom, about 3 minutes. Flip fish, one at a time, and continue to cook until tender when pressed in center and flesh is opaque, 2 to 3 minutes more. Using a slotted spatula, transfer fish to prepared baking sheet; sprinkle with salt. Between batches, increase heat and strain out browned crumbs, or wipe out pan as needed.
