Preheat an outdoor charcoal or gas grill. Alternately, heat a grill pan until smoking hot.

In a large bowl, combine together parsley, capers, garlic, oregano and red pepper flakes. Stir in the olive oil; season with salt and pepper. Set aside.

Place eggplant slices on the grill without overcrowding them. Cook the eggplants for 3 to 6 minutes and then turn them over. Cook for another 3 minutes or until eggplants are soft.

Dip each grilled eggplant slice into the balsamic vinegar and then transfer to a plate. Continue grilling and dipping the eggplant until all the slices are cooked and seasoned.

Spoon 2 tablespoons of the parsley mixture onto a platter and spread it out evenly. Arrange half of the grilled eggplant on the mixture in a single layer and then sprinkle more of the mixture on top of the slices. Place a second layer of eggplant on top and spread the remaining parsley on it. Cover with plastic wrap and refrigerate for at least 2 hours refrigerate for longer. Serve at room temperature.