How to Make It
Heat the oil in a large nonstick skillet until shimmering. Season the fish with salt and pepper and dredge in the flour, shaking off any excess. Add half of the fillets to the skillet and sauté over moderately high heat until lightly browned and cooked through, about 2 minutes per side. Transfer the fish to a warmed platter and repeat with the remaining fillets. Season with salt and pepper and sprinkle with the parsley; keep warm.
In a small skillet, cook the butter over moderate heat until fragrant and nut brown, about 3 minutes. Remove from the heat and add the lemon juice, shaking the skillet to blend. Pour the butter over the fish and serve.