Cut the eggplants into medium-sized cubes, sprinkle with coarse salt and leave to rest in a colander for at least 30 minutes, with a weight over them, then qwash under running water and pat them dry with a clean cloth.
In a large pan, fry the aubergines in abundant oil for 3 - 4 minutes, just enough time to have them golden brown. Use a slotted spoon to transfer the cubes on a plate covered with kitchen paper to absorb the oil in excess.
Place the sliced celery in a pot of slightly salted boiling water and blanch for 1-2 minutes. Drain and transfer to a sieve covered with a kitchen cloth.
Heat a large pan with the extra-virgin olive oil over medium-low heat. Add in chopped onion, garlic and tomatoes. Cook over low-heat until the onion is nicely caramelized and tomatoes are soft, about 5 minutes.
Add in the capers, olives, toasted pine nuts, fried eggplant and blanched celery. Add in the tomato paste and one tablespoon of water, if you feel it's getting too dry.
Sprinkle with sugar and drizzle with vinegar. Simmer until the vinegar has evaporated, then cover with a lid and cook for 10 minutes over low-heat, until all ingredients are cooked through.
Top your caponata with teared basil leaves and oregano, drizzle with extra-virgin olive oil and serve.