4 medium eggplants (about 2 lbs.), cut into ?-inch cubes
2 celery stalks, cut into ?-inch-long pieces
1 large red onion, thinly sliced lengthwise
6 oz. pitted green olives, halved
1/4 cup capers, rinsed and drained
1/4 cup tomato paste
1/2 cup red wine vinegar
2 tbsp. sugar
1/2 cup toasted whole almonds, finely chopped
Freshly ground black pepper
Extra-virgin olive oil, for drizzling
Place the eggplant in a colander, season liberally with salt, and toss to combine. Let the eggplant stand for 30 minutes, then rinse under cold running water until all the salt is gone. Squeeze all the moisture from the eggplant and dry them thoroughly on paper towels. In a large skillet, warm the olive oil over high heat. Working in three batches, add the eggplant to the oil and fry, tossing occasionally, until dark brown all over, about 10 minutes. Using a slotted spoon, transfer the eggplant to paper towels to drain and discard all but 2 tablespoons of the olive oil.
Reduce the skillet to medium heat, add the celery and onion, and cook, stirring, until soft, about 6 minutes. Stir in the olives and capers and cook for 2 minutes. Add the tomato paste and cook, stirring, until the paste is lightly caramelized, about 2 minutes more. Pour in the vinegar and sugar and cook, stirring, until the sugar dissolves and the vinegar almost completely evaporates, 2 to 3 minutes more.
Scrape the vegetables into a large bowl, stir in the eggplant and the almonds, and season the caponata with salt and pepper. Drizzle the caponata with extra-virgin olive oil before serving.