Place the fish, gray side up, on work surface. Using a paring knife, make an incision
Place flour onto a large shallow dish and season with salt and pepper. Press both sides of the fish into the flour, making sure it is fully coated. Shake off any excess flour. Heat the clarified butter in large saute pan over medium heat.
Set the fish, gray side down, in the pan and saute until golden brown, about 3 to 4 minutes. Use a fish spatula (or two large, wide spatulas) to carefully flip the fish and saute until golden brown and cooked throughout (the flesh should flake with a fork and the thickest part of the fish should be opaque), about 3 minutes more.
Drop the butter pieces into the hot pan, around the fish, let it melt and spoon it over the fish as it finishes cooking. When butter is frothy, squeeze the lemon over it (so the juice runs into the butter) and immediately spoon this over the fish. Sprinkle parsley over fish. (Alternatively, transfer fish to a platter and sprinkle with parsley before adding butter and lemon juice to the pan, swirling to combine.)
Fillet fish and serve immediately topped with sauce.