To make the caponata: In a heavy skillet heat 2 tablespoons of the oil over moderately- high heat until hot but not smoking. Cook the eggplant, stirring, for 3 to 5 minutes, or until it is tender, and transfer it to a bowl. To the skillet add the remaining 2 tablespoons oil and cook the onion and the celery over moderate heat, stirring, for 5 minutes. Add the olives, the capers, the vinegar, the sugar, the raisins, the pine nuts, and the tomatoes and cook the mixture, covered, stirring occasionally, for 5 to 10 minutes, or until it is cooked through and the celery is tender. Transfer to the bowl, cool, and chill, covered, overnight. Stir in the parsley and season the caponata with salt and pepper.
To make the bruschetta: Grill the bread on an oiled rack set about 4 inches over glowing coals for 1 minute on each side, brush the toasts on 1 side with the oil, and sprinkle them with salt, to taste.
Top each toast generously with some of the caponata, arrange 2 or 3 toasts on each of 4 plates, and garnish each serving with the parsley sprigs.