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1
Toss the aubergine cubes with fine salt and spread in a colander. Leave to drain for 30 minutes, then pat thoroughly dry with kitchen paper. The cubes should feel noticeably drier and slightly collapsed.
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2
Heat the abundant olive oil in a wide, deep frying pan over high heat. Fry the aubergine in batches — do not crowd the pan. This is where the dish lives or dies: the cubes must reach a deep, even golden colour and be cooked entirely through, caramelised at the edges and yielding at the centre when pressed. Under-fried aubergine will release its absorbed oil back into the sauce and ruin the texture of the finished dish. Remove with a slotted spoon and drain on kitchen paper.
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3
In a separate pan, warm the soffritto oil over medium heat and cook the onion gently until soft and translucent, without colour. Add the tomatoes and cook until reduced to a thick, cohesive sauce. The surface should show no pooling liquid.
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4
Blanch the celery slices briefly in boiling salted water — they should retain a distinct bite when pressed between finger and thumb. Drain immediately and set aside.
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5
Add the celery, olives, capers, pine nuts, and drained sultanas to the tomato base. Stir to combine and warm through over low heat for two to three minutes until the pan smells of a unified, briny-sweet sauce.
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6
Dissolve the sugar in the vinegar and pour over the pan. Stir through. Taste the agrodolce: the sweet and sour elements must be equally present and neither should dominate. Adjust with additional sugar or vinegar, a small amount at a time, until equilibrium is reached.
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7
Fold in the fried aubergine cubes gently, disturbing them as little as possible. Cook together over low heat for five minutes until everything is unified but the aubergine retains its form. Remove from heat, transfer to a serving dish, and leave to cool fully to room temperature. The caponata will be markedly superior after resting, covered, for 24 to 48 hours — the agrodolce should smell rounded and deep, not sharp, at that point.