Special equipment: an 18-by-13-inch sheet pan
Preheat the oven to 450 degrees F.
Put 2 tablespoons olive oil and the garlic in a large skillet and place over medium heat. When the garlic sizzles and its edges start to brown, add the tomatoes, red pepper flakes and 3/4 teaspoon salt. Bring to a simmer and continue to cook, stirring occasionally, until the sauce thickens, about 8 minutes. Remove from heat and stir in the chopped basil.
Heat an 18-by-13-inch sheet pan in the oven for at least 10 minutes while you bread the eggplant. Line up 3 shallow dishes; fill one with the flour, one with the beaten eggs, and one with the breadcrumbs. Sprinkle both sides of the eggplant slices with salt. Dredge an eggplant slice in the flour (tapping off excess), then dip in the egg, and finally dredge it in the breadcrumbs. Repeat with the remaining eggplant.
When all the eggplant slices are breaded, carefully remove the heated sheet pan from the oven and brush it with 2 tablespoons olive oil. Place the eggplant on the sheet pan in a single layer. Bake until the undersides are crisp and browned, 8 to 10 minutes, then flip the slices and continue baking until they are golden on the second side, 8 to 10 minutes more.
Top the baked eggplant with the tomato sauce, mozzarella and Parmesan. Return the pan to the oven and bake, rotating halfway through, until the cheese melts and browns and the sauce is bubbly, 20 to 25 minutes. Top with torn basil before serving.
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