First make the Parsley Butter. Cream the butter, stir in the parsley and a few drops of lemon juice at a time. Roll into butter pats or form into a roll and wrap in greaseproof paper or tin foil, screwing each end so that it looks like a cracker. Refrigerate to harden.
Heat the grill-pan. Dip the fish fillets in flour which has been seasoned with salt and freshly ground pepper. Shake off the excess flour and then spread a little butter with a knife on the flesh side, as though you were buttering a slice of bread rather meanly. When the grill is quite hot but not smoking, place the fish fillets butter side down on the grill; the fish should sizzle as soon as they touch the pan. Turn down the heat slightly and let them cook for 4 or 5 minutes on that side before you turn them over. Continue to cook on the other side until crisp and golden. Serve on a hot plate with some slices of Parlsey Butter and a segment of lemon.
Parsley Butter may be served directly on the fish, or if you have a pretty shell, place it at the side of the plate as a container for the butter. Garnish with parsley and a segment of lemon.