Put a wide cast-iron pan over medium-high heat. Add 4 tablespoons olive oil to coat bottom of the pan. When oil is rippling and hot, test a piece of eggplant to see that it sizzles and turns brown immediately. Add the eggplant in batches in a single layer. Turn the eggplant and brown on all sides. Don’t let the pan get too hot. Remove the eggplant to a plate lined with paper towels and continue with additional oil and the remaining eggplant. Season the eggplant with salt. (Alternatively, roast the eggplant on a baking sheet at 400F, lightly drizzled with oil, until cooked and golden brown, about 20 minutes.)
Place a frying pan on medium high heat and cook the onions, lightly sprinkled with salt and stirring occasionally, until the onions are soft and lightly golden, 7 minutes. Add the celery, tomato paste, tomatoes, capers, and olives. Season with salt and pepper. Cook, stirring often, until the vegetables begin to turn golden brown, 10 minutes.
Add the crushed red pepper, red wine vinegar, sugar and wine and simmer for 5 minutes. Gently fold in the eggplant and simmer for 3 to 4 minutes more. Taste and season if needed with additional salt, pepper and vinegar.
Let sit 1 hour at room temperature before serving. Sprinkle with parsley and serve.