The name of this familiar Italian specialty is misleading. The term alla parmigiana means “in the style of Parma” (or “of a woman of Parma”), but the dish has nothing to do with the cooking of that famous city in Emilia-Romagna. It is a southern Italian dish, claimed by both Sicily and Naples — probably the two parts of Italy where eggplant is eaten most.
The familiar explanation for the name is that the dish usually includes, in addition to the mozzarella that is its second most-important ingredient, a sprinkling of Parmigiano-Reggiano. If that were the case, though, it would be “al [or col] parmigiano.” A more likely explanation seems to be that “parmigiana” is a corruption of a Sicilian dialect word for the pattern of wooden slats that overlap in window shutters (like the slices of eggplant in this dish) — palmigiana (according to Mary Taylor Simeti) or parmiciana (according to Anna Pomar).
Italian American versions of this dish often fry the eggplant slices first in an egg batter or breadcrumbs, but that is rare in Italy.
*Note: You can also substitute one 28-ounce can whole San Marzano tomatoes, drained and finely chopped, for every 2 cups of tomato sauce.
Heat 3 tablespoons of the oil in a medium-sized saucepan over medium heat. Add the garlic and cook, stirring frequently, until it begins to color, 1-2 minutes. If using the tomato sauce, stir it into the garlic and oil and cook for 2-3 minutes. Julienne 6 of the basil leaves and add them to the pan. Cook for 5 more minutes, then set aside. (If using the canned tomatoes, add them to the garlic and oil, season with salt and pepper, reduce the heat to medium-low, and simmer, stirring frequently, until thickened to a sauce, about 30 minutes. Stir in the julienned basil during the last 5 minutes of cooking.) Set the sauce aside.
Preheat the oven to 375 degrees.
Heat the remaining oil in a large frying pan over medium-high heat. Working in batches, add the eggplant slices and fry, turning them once, until soft and golden brown, 2-3 minutes per side. As the eggplant is finishes cooking, drain it on paper towels.
Spread a layer of the tomato sauce over the bottom of a 9-by-13-inch baking dish. Cover the sauce with a layer of eggplant slices, overlapping them slightly. Arrange slices of the mozzarella over the eggplant, then spread another layer of tomato sauce on top of the cheese. Repeat the process to use all the tomato sauce, eggplant, and mozzarella, ending with a layer of sauce. Scatter the whole basil leaves over the sauce, then sprinkle the Parmigiano over the top.
Bake until the sauce is bubbling and the cheese is golden brown, 25-30 minutes. Serve immediately.