Prep eggplant. Toss the diced eggplant with 1 Tbsp salt. Set in a colander for 30 minutes. Rinse and pat very dry.
Brown eggplant. Heat 4 Tbsp oil in a wide pan over medium-high. Cook eggplant in 2–3 batches until golden and tender, 6–8 minutes total. Transfer to a plate.
Soft-cook veg. Add remaining 2 Tbsp oil to the pan. Sauté onion and celery with a pinch of salt until soft, 5–6 minutes. Stir in garlic for 30 seconds.
Make the sauce. Add tomatoes and tomato paste. Simmer until thick and saucy, 8–10 minutes.
Add the sweet-sour. Stir in olives, capers, vinegar, sugar, and red pepper flakes. Simmer 2 minutes.
Combine. Return eggplant to the pan. Stir gently. Simmer on low until glossy and jammy, 8–10 minutes. Season with salt, pepper, and more vinegar/sugar to balance.
Rest and serve. Let it cool to warm or chill. Top with basil or parsley. Serve with crusty bread, grilled fish/meat, or over pasta/rice.