Cut eggplant into ¾-inch cubes.
Deep fry the eggplant in ⅔-inch layer of oil, over high heat, until dark gold. With a slotted spoon, remove eggplant cubes from pan, drain on paper towels and set aside.
Transfer 3 Tablespoons of the frying oil to a large skillet. Set aside the remaining oil.
Heat the oil then add peppers, large pieces of onion and celery.
Cook over moderate heat, stirring, for a couple of minutes.
Reduce heat to low, cover and cook for 8 minutes.
Uncover, increase heat to high and cook, stirring, until vegetables start browning.
Add capers, olives, vinegar and sugar; then turn off heat.
Add eggplant and mix very gently.
Heat 2 Tablespoons of the oil used to cook the eggplant in a small pan and sauté the finely chopped onion. Add the tomatoes.
Cook over high heat until they sizzle.
Stir in salt and add to the vegetable mixture.
Add pine nuts to the mixture.
Stir gently until all the pieces are evenly distributed.
Put into your favorite serving bowl and sprinkle with chopped parsley.
Serve at room temperature.