This dish gets its name from the vessel in which it's cooked. A tièdda, or tiella or teglia, is a round earthenware baking dish that is deep enough for layering a number of ingredients. The one constant in the dish is potatoes; for best results, use waxy red-skinned potatoes or semi-waxy Yellow Finns but not starchy baking potatoes like Idahos.
At Trattoria Casareccia, a wonderful little home-style restaurant in Lecce, the owner, Concetta Cantoro, makes this tièdda with zucchini and mussels; others might substitute salt cod for the mussels or add a layer of wild mushrooms. The recipe may seem complex, but the mussels, tomato sauce and potatoes can be prepared well ahead of time.
Preheat the oven to 375°. Place the mussels in a deep skillet and add 3 tablespoons of water. Cook over moderately high heat, stirring frequently. As the mussels just open, transfer them to a large platter with a slotted spoon. (They will continue cooking later.) Strain the liquid through a sieve lined with several layers of dampened cheesecloth and reserve. (You should have about 1/4 cup of liquid.) Remove the mussels from their shells.
Heat 2 tablespoons of the olive oil in a large nonreactive skillet. Add half of the sliced onions and all of the garlic and cook over low heat until softened but not browned, about 7 minutes. Add the tomatoes, raise the heat to moderate and cook until they have cooked down to a thick sauce, about 10 minutes.
Meanwhile, bring a medium sauce-pan of water to a rolling boil. Add the potato slices and cook until just tender, 7 to 10 minutes. Drain well.
Brush the bottom of a deep 2-quart ceramic baking dish with 1 tablespoon of the olive oil. Spread one-third of the tomato sauce over the bottom. Top with half of the remaining raw onions followed by half of the mussels, zucchini slices and potatoes. Sprinkle with one half of the parsley, basil, oregano, 1 tablespoon of the olive oil and salt and pepper. Cover with another third of the tomato sauce and repeat the layering with the remaining ingredients, ending with the tomato sauce. Sprinkle the bread crumbs, grated cheese and the remaining olive oil over the top.
In a small bowl, combine the reserved mussel liquid with 1/4 cup of hot water. Pour the liquid gently down the side of the baking dish to keep the vegetables from sticking. Cover the dish with a double layer of aluminum foil and bake for about 1 hour, or until the potatoes are very tender; remove the foil during the last 15 minutes to brown the top. Let cool slightly, then serve hot or at room temperature.