Add the pine nuts to a large frying pan. Heat it up on medium to high heat and toast them until golden brown [approximately two to three minutes]. Set the pine nuts aside and allow them to cool down.

In a glass, mix the white wine vinegar, white sugar, and tomato paste together. This is the 'agrodolce sauce' [sweet and sour sauce], which will be added at the end of cooking. Set it aside for later use.

Halve the pitted green olives. Wash and roughly chop the vine tomatoes.

Wash the eggplants and cut them length-wise in slices approx ½" thick [1-1.5cm]. Layer the slices in a large colander, with some salt in between each layer. If you have it, opt for rock salt, as it will be easier to remove afterward. Weigh the eggplant slices down using something heavy, like a bowl filled with water or a bottle of olive oil, and allow it to drain for 30 minutes. This process will help remove the excess moisture, which could make the eggplant watery, and remove any bitterness the eggplant may have.

Once done, remove the excess salt using a clean wet teatowel or cloth. Don't wasj them under running water as eggplant is like a sponge, and it would absorb some water again.

Finally, cut the slices into cubes, and deep fry them in batches in sunflower oil until they are golden brown [approximately 3-4 minutes per batch]. When removing them from the oil, lay them on some paper towel, so that the excess oil can be removed.

Add the olive oil a large skillet or saucepan, and heat it up on medium heat. Once warm, add the thinly sliced onions, and sautee them until they become translucent [2-3 minutes].

Next, add the chopped celery to the saucepan, and mix well. Allow the celery to cook for 3-4 minutes, until it starts to soften.

The tomatoes will now be soft, and all the ingredients cooked, so you can now add the sweet and sour sauce to the pan.

Increase the heat to high, and mix the sauce well until the pungent smell of vinegar has gone.

Finally, add the fresh basil leaves and fried eggplant to the sauce, and mix well.

Allow the eggplant caponata to cool to room temperature before serving - and enjoy!