For the sauce: Heat the oil in a heavy medium saucepan over medium. Add the garlic, shallots and salt. Stir until fragrant, about 2 minutes. Add the tomato sauce, basil, oregano and crushed red pepper. Simmer the sauce until the flavors blend and the sauce thickens, stirring often, about 5 minutes. Mix in the vinegar.
For the eggplant: Mix the flour, salt and pepper in a shallow bowl. Place the panko breadcrumbs in another shallow bowl. Whisk the egg whites in a medium bowl until frothy. Dip each eggplant slice in the flour mixture, then into the beaten egg whites, and then into the panko breadcrumbs to coat completely.
Heat the oil in a heavy medium skillet over medium-high heat until hot (the surface will appear to be shimmering), 2 to 3 minutes. Add half of the eggplant slices. Cook until deep golden brown, 1 to 2 minutes per side. Transfer the eggplant to a paper-towel-lined plate. Fry the remaining eggplant. (Can be made 1 hour ahead. Let stand at room temperature.)
Preheat a broiler. Toss the mozzarella and Parmesan in a small bowl until well blended. Spread 1 generous teaspoon of the sauce over each eggplant slice. Top with a rounded teaspoon of the cheese mixture; spread out to cover and press lightly to adhere. Transfer the eggplant slices to a rimmed baking sheet. Broil until the cheese has melted, 1 to 2 minutes. Transfer the mini eggplant parmesans to a platter and garnish each with small basil leaf. Let stand 2 to 3 minutes before serving.
For a smoother consistency, the sauce can be pureed in a blender or food processor.
Recipe courtesy of Giada De Laurentiis