Place the oil in a heavy medium saucepan. Add add the shallot and garlic to the saucepan. Stir over medium heat until very fragrant, about 2 minutes. Add the tomato sauce, basil, oregano, and crushed red pepper. Simmer the sauce until flavors blend and the sauce thickens slightly, stirring often, about 5 minutes. Mix in the vinegar, salt, and pepper, then more vinegar if desired. Puree sauce in blender. (Can be made 2 days ahead. Cool, cover, and chill.)
Place flour and panko in medium bowls. Whisk egg whites in a third medium bowl until broken up and very frothy. Dip each eggplant slice in flour, then egg white, then panko to coat completely. Arrange eggplant on paper towels. (Can be made 2 hours ahead. Let stand at room temperature.)
Preheat the oven to 350°F. Heat the oil in a heavy medium skillet over medium-high heat for 2 to 3 minutes until hot (the surface will appear to be shimmering). Add half of eggplant. Cook until deep golden brown, 1 to 2 minutes per side (or more if needed). Carefully (so the crispy crust does not break) transfer the eggplant to a paper towel lined plate. Fry the remaining eggplant. (Can be made 1 hour ahead. Let stand at room temperature.)
Toss the cheeses in a small bowl until well blended. Spread 1 generous teaspoon of sauce on each eggplant slice. Top each with a rounded teaspoon of cheese mixture; spread out to cover and press lightly to adhere. Transfer the eggplant slices to a rimmed baking sheet. Bake until the cheese mixture melts and the eggplant is heated through and crisp, about 12 minutes. Transfer the mini eggplant Parmesans to a platter. Garnish each with 2 small basil leaves. Let stand 2 to 3 minutes to cool a bit and serve.