In a large, heavy-bottomed saucepan, heat the oil until almost smoking. Carefully add the eggplant medallions, working in batches to avoid overcrowding the pan and lowering the heat of the oil. Cook eggplant until golden brown on both sides and remove pieces as they're finished to a sheet tray lined with paper towels. Set aside.
In a 12 to 14 inch saute pan, heat 2 tablespoons olive oil until almost smoking. Add the onions and celery and saute until light golden brown. Remove from heat and add the vinegar, sugar and salt and pepper to taste. Place the cooled eggplant slices in a large bowl, cover with the vinegar mixture and let sit 1 hour before serving at room temperature.