How to Make It
In a large skillet, heat 2 tablespoons of the olive oil. Add half of the eggplant slices and fry over moderately high heat until golden brown, about 2 minutes per side. Transfer the fried eggplant to a rimmed platter lined with paper towels and season with salt and pepper. Repeat with 2 tablespoons of olive oil and the remaining eggplant slices. Discard the paper towels.
In a small bowl, mix the sherry vinegar with the chives, the parsley, the tarragon, the garlic and 1 tablespoon of the olive oil. Season the marinade with salt and pepper. Pour the marinade over the fried eggplant and turn to coat the slices. Let stand at room temperature for at least 10 minutes.
In a large skillet, heat 1 tablespoon of the oil. Season the pork with salt and pepper. Add half of the pork slices to the skillet and cook over high heat until golden and no longer pink in the center, about 1 minute per side. Transfer to a plate. Repeat with the remaining tablespoon of olive oil and the remaining pork.
Set 2 large cast-iron skillets over moderately high heat for about 5 minutes, or until very hot. Spread 2 teaspoons of butter on one side of each slice of bread. Lay 6 slices on a work surface, buttered side down. Top each of the slices with one-sixth of the pork and pickled eggplant and 2 slices of cheese. Close the sandwiches with the remaining bread slices, buttered side up.
Place a sandwich in each cast-iron skillet and set a second heavy skillet directly on top of the sandwich. Set a large, heavy can in each skillet to weigh the sandwich down. Cook the panini over moderately high heat for 3 minutes. Flip each sandwich and cook for about 3 minutes longer, or until browned and crisp all over. Transfer the panini to a cutting board and cut them in half. Repeat with the remaining panini, reducing the heat to moderate.