The vegetables in this sweet-and-sour sautéed eggplant caponata are cooked together until soft and tender, so their flavors meld and intensify. The eggplant takes the longest to cook, so sauté it first and then combine it at the end of cooking with the browned aromatics. Serve warm, atop crostini or with grilled meats or fish.
Line a large rimmed baking sheet with paper towels, top with the eggplant, and sprinkle with 1 tsp. salt and ½ tsp. pepper. Shake to toss, and then let sit for 10 minutes to sweat out some of the eggplant’s moisture.
Set a 12-inch nonstick skillet over medium-high heat for 1 minute. Add 3 Tbs. of the olive oil, and once it’s shimmering hot, about 1 minute, add the eggplant. Cook, tossing occasionally, until the eggplant starts to brown in places and becomes tender, about 5 minutes. Transfer to a large plate.
Reduce the heat to medium, add another 3 Tbs. olive oil, the onion, pepper, and celery, sprinkle with 1 tsp. salt, and cook, stirring, until the onion softens and browns in places, about 8 minutes.
Fold in the tomato paste, sugar, and garlic, and cook for 1 minute, tossing, to incorporate. Add the sautéed eggplant, raisins, vinegar, and capers, and cook, tossing, for 2 to 3 minutes, so that the flavors come together and all of the vegetables are soft.
Fold in all but 2 Tbs. of the parsley, and season to taste with salt and pepper. Serve sprinkled with the remaining 2 Tbs. olive oil and parsley.