Preparation

• Cut the eggplant crosswise into 1/4-inch-thick slices. Put the slices in single layers between paper towels on rimmed baking sheets, sprinkling each layer lightly with the salt. Set aside for 1 hour.
• Put 1/2 cup of the oil in a large skillet, and heat on medium until the oil shimmers. Pat the eggplant dry with paper towels. Fry the eggplant in single layers in batches until light golden and soft in the center when pierced with a fork, 2 to 2-1/2 minutes per side. When the eggplant is tender, transfer to rimmed baking sheets lined with paper towels, replenishing the oil in the skillet as necessary.
• Position a rack in the center of the oven, and heat the oven to 350°F.
• To assemble, spread about 1/4 cup of the marinara sauce evenly on the bottom of a 3-qt. 9×13-inch baking dish. Pat the eggplant with paper towels, and lay enough slices to cover the bottom of the baking dish in a single layer. Sparingly dollop 2 to 3 Tbs. of sauce on top of some of the eggplant slices, scatter a generous handful (about 3/4 cup) of the mozzarella over the eggplant, top evenly with some of the basil (about 1/4 cup), and then sprinkle with 1/4 cup of the grated cheese and a few grinds of pepper. Continue layering in this way until the final layer of eggplant is used. Finish with the remaining tomato sauce, grated cheese, and a few grinds of pepper.
• Bake until the sauce is bubbling and the cheese is lightly browned, about 45 minutes. Let cool for 35 to 40 minutes before slicing and serving.