In a large skillet, heat ½ cup of the olive oil to medium and add the chopped eggplant. Toss the eggplant to evenly coat in oil. Sauté, stirring frequently, until eggplant has browned, begins cooking down, and is soft, about 10 minutes.
Pour the eggplant into a bowl and set aside.
Place the skillet back on the stove and add ¼ cup of oil. Add the onion and celery and saute, stirring every couple of minutes, until veggies are cooked through, about 8 to 10 minutes (you want the eggplant to be soft, but still maintain its form).
Add the garlic and sauté another 2 minutes.
Add the remaining ingredients and stir everything together. Bring mixture to a full boil, reduce the heat, and allow the sauce to boil gently (uncovered) until much of the liquid has been reduced, about 15 minutes.
Serve hot over spaghetti squash, toasted bread, or serve cold. Keep leftovers in the refrigerator for up to 5 days – the caponata tastes better the longer it sits!