To Prepare the Roasted Eggplant Terrine:
Preheat the oven to 425 degrees.
Cut the stem ends off all the eggplants. Cut 3 eggplants in half lengthwise and score the flesh with a sharp knife, making sure you don’t cut through the skin. Rub the cut surfaces of the eggplants well with ½ tablespoon of the salt. Set the eggplant halves aside on paper towels, cut side down, and let them drain for 10 to 15 minutes.
Cut the fourth eggplant in half lengthwise and cut into ¼-inch lengthwise slices. Sprinkle with the remaining salt. Lay the slices on top of one another in a colander. Place a dish on top and weight it with about 1½ pounds. (A 28-ounce can of tomatoes will do.) Let drain for 20 minutes.
Line two 18 x 13-inch baking sheets with parchment paper. Dry the cut surfaces of the 6 eggplant halves and brush a thin film of oil over the parchment and the entire cut surface of each eggplant half, using 3 tablespoons of the olive oil. Place the eggplant halves on the baking sheets, cut side down, and roast in the preheated oven 45 to 55 minutes. The eggplants are completely cooked when they dent easily as you poke the skin. Do not cook them more than 1 hour, as they burn easily once they are cooked. Remove them from the oven and let cool for a few minutes.
Once the eggplant halves have finished roasting, dry the eggplant slices with a paper towel and line another sheet pan with parchment paper. Brush the paper and the eggplant slices with the remaining olive oil and cook them in the oven for 25 to 35 minutes, until golden brown. Set aside.
Using a large spoon, scoop the cooked flesh out of the roasted eggplant halves. Discard the skin and place the flesh in a colander with a bowl underneath to catch the juice. Let drain for 40 minutes, stirring once. Save 1 cup of the juice that has drained from the eggplant to use in the sauce. Discard the rest or save it for other uses.
Now we’re ready to assemble our terrine.
Preheat the oven to 400 degrees.
Separate the 4 eggs. Mix the yolks, Pecorino cheese and 1 cup of the breadcrumbs with the roasted eggplant flesh. Beat the egg whites until they form stiff peaks, then fold them gently into the eggplant mixture.
Rub the inside of a standard glass loaf pan (8½ x 4½ x 2½ inches) with the butter and coat with the remaining breadcrumbs. Line the bottom of the loaf pan with the 2 largest slices of the reserved eggplant; place the remaining slices around the edges, standing up and overlapping slightly. They should extend above the rim by about a third of their length so that you can fold them over the roasted filling.
Put half of the eggplant mixture into the pan as the first layer and top it with the goat cheese as the middle layer. Cover with the remaining eggplant mixture and fold over the overlapping eggplant slices. Bake in the preheated oven for 45 minutes.
This dish can be served right away by inverting it onto a serving tray and cutting it at the table, but I strongly recommend that you let it rest at least overnight in the refrigerator. When ready to serve, invert it onto a cutting board, cut into serving slices, and reheat in a preheated 325-degree oven on a parchment-lined sheet pan for 10 to 15 minutes. It can be prepared up to 4 days in advance.
To Prepare the Roasted Eggplant Sauce:
Process the tomato sauce and eggplant juice in a food processor for about 2 minutes. Strain through a wire-mesh strainer into a saucepan. Add the sugar, basil and mint, and bring to a simmer over medium heat. Reduce the heat to medium-low and cook for 10 minutes, stirring twice.
Heat the olive oil in a nonstick pan set on high heat until sizzling. Add the celery and sauté until brown. Drain well and add to the simmering sauce. The sauce is now complete. It can be made up to 4 days in advance and kept in the refrigerator. Heat through before serving.
Pour a pool of the hot sauce on each dinner plate and place a slice of the eggplant terrine on top.
For the Roasted Eggplants:
4 eggplants, about 1½ pounds each
¾ tablespoon salt, divided
4 tablespoons olive oil, divided
1 cup grated Pecorino cheese
1¼ cups Italian-style breadcrumbs, divided
1 tablespoon butter
¼ pound crumbled goat cheese
For the Roasted Eggplant Sauce:
2 cups tomato sauce
1 cup reserved roasted eggplant juice
2 tablespoons chopped fresh basil
1 tablespoon chopped fresh mint
1 tablespoon olive oil
6 tablespoons finely diced celery