Place the eggplant cubes in a colander and toss with the salt. Let sit for 30 minutes. Rinse quickly if heavily salted, then dry very well with paper towels or a clean kitchen towel. Do not leave the eggplant wet. Dry eggplant browns properly and absorbs less oil. That salting stage draws out real, considerable moisture through osmosis, and the thorough drying that follows removes it before it ever has the chance to interfere with proper browning or cause excess oil absorption.

Bring a small pot of salted water to a boil. Blanch the celery for 2–3 minutes until just slightly tender but still with bite. Drain and set aside. Celery should stay vivid and slightly firm, not soft and floppy. That genuinely brief blanching time is calibrated specifically to soften the celery just enough while protecting both its own vivid colour and its crisp-tender bite from turning dull and limp.

Toast the pine nuts in a dry pan over medium-low heat for 2–4 minutes, stirring often, until lightly golden. Remove immediately and set aside. That immediate transfer off the hot pan protects the pine nuts from their own real, narrow margin between properly toasted and burnt, given how quickly residual heat alone can push them past that point.

Heat a generous layer of neutral oil in a wide skillet over medium-high heat. Fry or shallow-fry the eggplant in batches until golden-brown and softened, about 6–8 minutes per batch. Transfer to a tray or plate lined lightly to drain excess oil. Do not overcrowd the pan. If the pan is crowded, the eggplant steams instead of browning. The goal is a soft interior, caramelized edges, cubes still holding shape. Frying in properly small, uncrowded batches protects the oil's own temperature from dropping too far when multiple pieces are added at once — a significant drop lets the eggplant absorb excess oil rather than actually browning and developing colour.

Discard excess oil from the skillet and add 2 tbsp olive oil. Cook the onion over medium heat for 4–5 minutes until softened but not deeply browned. Add the tomatoes and tomato paste if using. Cook for 5–7 minutes until the tomatoes break down and the mixture thickens slightly. Add the blanched celery, olives, and capers. Cook for 2 minutes. Cooking these aromatics in the same skillet the eggplant just used means the base picks up real, residual flavour from whatever fond was left behind, rather than starting from a clean, neutral pan.

In a small bowl or cup, stir together the sugar and vinegar until mostly dissolved. Pour this into the pan and simmer for 1–2 minutes so the sharp raw vinegar edge cooks off slightly. The result should taste balanced — clearly sweet-sour, but not harshly vinegary and not dessert-sweet. That brief simmer is what lets the vinegar's own sharpest, rawest edge actually cook off into the air, protecting the finished agrodolce from tasting harsh rather than properly balanced.

Return the eggplant to the pan and fold gently to coat without mashing it. Add most of the toasted pine nuts and the torn basil. Cook for 1 minute, then remove from the heat. Taste and adjust with black pepper, a little more vinegar, or a pinch more sugar if needed. Let cool for at least 20–30 minutes before serving. Caponata is best warm-room temperature or fully room temperature, not piping hot. That deliberately gentle folding protects the eggplant's own real, browned structure from being mashed apart — vigorous stirring at this stage would break the cubes down into something closer to a puree, losing the distinct, chunky texture caponata is specifically built around.