Heat the griddle 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.
Meanwhile, make the sauce. Melt the butter and allow to boil.
Put the egg yolks into a bowl, add the mustard, wine vinegar and the herbs, mix well.
Whisk the hot melted butter into the egg yolk mixture little by little so that the sauce emulsifies. Keep warm, by placing the heatproof bowl in a saucepan of hot but not boiling water.
Serve the mackerel with the sauce, a good green salad and new potatoes.