Place the egg yolks in a blender, food processor or deep bowl.

Blend in the salt, pepper and mustard. If blending by hand, use a small whisk.

If using the machine, pour the oil through the funnel in a thin, steady stream with the machine running. If mixing by hand, add oil a few drops at a time, beating well in between each addition.

When half the oil has been added, the rest may be added in a thin steady stream while beating constantly with a small whisk.

Mix in the relish, parsley, lemon juice and Tabasco. Beat the egg whites until stiff but not dry and fold into the mayonnaise.

Grill the fish about 2 inches from the heat source for about 6-10 minutes, depending on the thickness of the fillets.

Spread the sauce over each fillet and grill for 3-5 minutes longer, or until the sauce puffs and browns lightly

When preparing the mayonnaise either by machine or by hand, do not add the oil too quickly or the mayonnaise will curdle. If it does curdle, beat another egg yolk in a bowl and gradually beat in the curdled mixture. This should bring it back together again.