Wash and dice the eggplant, but don’t peel them;
Place the eggplant pieces into a strainer or directly in the kitchen sink;
Generously sprinkle with salt, and allow them to sit for 1 hour;
Wash and dice the celery into very small pieces;
Immerse the celery in boiling water for 2 minutes, drain it while still crisp and save the water as you will need it for the tomatoes;
Bring the water to a boil again, immerse the tomatoes for 30 seconds, or until the skins start to peel back, and rinse them under cold running water; peel the tomatoes, discard the seeds, and cut them into coarse pieces;
Toast the pine nuts in a nonstick pan for a few minutes. Stir them so that they don’t burn;
Halve and pit the olives;
Sweat the onion (cook them over very low heat until they turn translucent) in a large hot skillet with two tablespoons of oil;
When the onion turns golden, add the tomatoes and the tomato paste; cook over medium heat without a lid for about 10 minutes;
Season with salt and pepper and add the celery, the olives, and the capers (rinse away all the salt before using them);
Cook for about 3-4 minutes;
Dissolve the sugar in the vinegar. Stir well and pour it on the vegetables;
Let simmer until reduced;
Cook over medium-low heat for about 20 minutes until all the flavors are well combined and the sauce gets smooth and thick;
Rinse the salt off the eggplant in cold running water;
Pat the eggplant dry with a paper towel;
Fry the eggplant pieces in plenty of very hot extra virgin olive oil in two or three batches;
When they turn golden, take them out with a skimmer and place the pieces on a tray lined with a paper towel in order to remove the excess oil;
When you have fried all the eggplant, add the pieces to the other vegetables; stew over low heat for 5 minutes;
Add the toasted pine nuts;
Wash and add the basil leaves;
Stir well and cook for a few more minutes so that they absorb all the flavor;
Garnish with some basil leaves and pine nuts and enjoy your caponata.