Detach and discard the leeks’ green tops. Slice the lower white parts of the stalks into very thin rounds. The yield should be about 4cups.
Put the sliced leeks into a medium sauté pan or skillet, add the olive oil, sprinkle with salt, and put in ⅓cup of water. Cover the pan, turn on the heat to low, and cook, stirring from time to time, until the leeks are reduced to a soft pulp. When done, with the heat turned off, put 2tablespoons of butter into the pan, stirring it into the warm leeks to melt it.
Turn on the oven to 450°.
Peel the potatoes, slice them very thin, wash in cold water, and pat dry with kitchen toweling.
Choose a baking dish that can later accommodate the bluefish fillets laid out flat without overlapping, and lightly smear the bottom with about ½tablespoon of butter.
Put the potato slices and all the leeks and juices from their pan into the baking dish and sprinkle with salt and pepper. Mix thoroughly and spread evenly over the bottom of the dish. Place the dish in the preheated oven and bake for 35 minutes until the potatoes are tender and a light crust has formed on their edges.
Combine the grated Parmesan and bread crumbs, sprinkle about 2 to 3tablespoons of the mixture over the potatoes and leeks in the baking dish, and continue baking for another 5 to 7 minutes.
Lay the fish fillets, skin side down, flat over the potatoes and leeks, sprinkle the remaining Parmesan and bread crumb mixture over them, and dot with the remaining butter. Return the dish to the oven and bake for about 10 minutes, or slightly longer if the fillets are thicker than ½inch.
Turn on the broiler and place the dish under it (do not let the flame or heating element touch or even come close to the dish unless it’s flameproof) for about 3 minutes until a light crust has formed over the fish. Before serving, let the heat subside for 2 or 3 minutes.