Prepare Grilled or Broiled Fish Fillets. Stir 2 tablespoons chopped herbs (any combination of parsley, chervil, basil, thyme, and/or fennel fronds) into the olive oil or melted butter or use Charmoula instead of the olive oil or butter. If the fillets are ½ inch thick or less, spread this paste on them before broiling. Rub thicker fillets with some olive oil or melted butter before cooking and spread the herb paste on them 3 or 4 minutes before they are done.