For the eggplant: Slice the eggplant in half lengthwise, and then into 1/4-inch half-moon slices. Put on a cookie sheet lined with paper towels and sprinkle with salt. Allow the salt to extract some of the moisture from the eggplant slices for at least 10 minutes while you prep the rest of your ingredients.
Take three plates and fill one with the flour, one with the beaten eggs and the third with the breadcrumbs. Dry the eggplant slices with the paper towels. Then coat each slice in the flour, then the eggs and finishing with the breadcrumbs. Allow these slices to rest for a minute; this will make the coating stick a little better and dry out to make a crispier crunch.
Coat a large nonstick skillet over medium heat with enough vegetable oil for shallow frying. Fry the eggplant slices in batches until golden brown, about 3 minutes on each side. Remove from the oil and drain on paper towels. Season with salt and pepper as soon as soon as they come out. Allow to cool completely.
For the tomato concasse: In a saute pan, heat the olive oil over medium heat. Add the onions, oregano and chile flakes if using, and cook until translucent, about 3 minutes. Add the garlic and cook for another minute. Add the tomatoes, lower the heat and simmer until the sauce is thick and chunky, about 10 minutes. Cool completely.
For the empanadas: Preheat the oven to 375 degrees F. Roll out each sheet of puff pastry dough to a 12-by-12-inch square and cut four 6-inch rounds out of each sheet. Place 1 slice eggplant in the middle of the dough round. Top with a tablespoon of tomato concasse, followed by a piece of the mozzarella cheese. Fold the dough over and seal using the back of a fork. Whisk the egg with a little water and brush the empanadas. Sprinkle a little dried oregano and the Parmesan on the tops. Bake until golden, about 15 minutes.
Puree the remaining tomato concasse; that'll be your dipping sauce for the empanadas.