Wash the fish in cold water, inside and out. If using a fish fillet, separate it into two halves, remove the bones, but leave the skin on.

Cut off the finocchio tops down to the bulbs, and discard them. Trim away any bruised, discolored portion of the bulbs. Cut the bulbs lengthwise into thin slices less than 1/2 inch thick. Soak them in cold water for a few minutes and rinse.

Choose a sauté pan that can subsequently accommodate all the fish. Put in the olive oil, the sliced finocchio, salt, about 1/2 cup water, and turn on the heat to medium. Cover the pan and cook for 30 minutes or more, depending on the freshness of the finocchio, until it is completely wilted and very tender. If after 20 minutes, the finocchio appears still to be hard when prodded with a fork, add 1/4 cup water.

When the finocchio is tender, uncover the pan, and turn up the heat to boll away completely any liquid left in the pan. Turn the finocchio slices frequently until they become colored a deep gold on both sides. Add a few grindings of pepper, turn the heat down to medium, and Push the finocchio to one side to make room for the fish in the pan.

Put in the fish, skin side down if you are using fish fillet, sprinkle with liberal pinches of salt and grindings of pepper, and spoon some of the oil in the pan over it. Cover and cook for 6 to 7 minutes. Then gently turn the fish over, baste again with olive oil, cover, and cook another 5 minutes or so, depending on the thickness of the fish.

Transfer the fish to a platter and pour the entire contents of the pan over it. If using whole fish, you might prefer to fillet it before placing it in the serving platter. It's not difficult to do: Separate the fish into two lengthwise halves, pick out the bones, use a spoon to detach the head and tail, and it's done. Remember to cover with all the finocchio slices and juices from the pan.