Preparation Mix tomatoes, celery, onion, olives, chopped oregano, capers, garlic, and crushed red pepper in medium bowl. Whisk red wine vinegar and 1 tablespoon extra-virgin olive oil in small bowl; pour over tomato mixture and toss to coat. Season caponata to taste with salt and pepper. DO AHEAD: Caponata can be prepared 2 hours ahead. Let stand at room temperature. Prepare barbecue (medium-high heat). Peel eggplant lengthwise to create alternating 2-inch-wide intervals of peeled and unpeeled skin. Cut eggplant crosswise into 6 slices, each about 1 inch thick. Brush eggplant slices with oil; sprinkle with salt and pepper. Grill eggplant slices until slightly charred and very tender when pierced with knife, about 8 minutes per side. Place 1 grilled eggplant slice on each of 6 plates. Spoon caponata over, garnish with oregano sprigs, and serve warm or at room temperature.
Preparation Mix tomatoes, celery, onion, olives, chopped oregano, capers, garlic, and crushed red pepper in medium bowl. Whisk red wine vinegar and 1 tablespoon extra-virgin olive oil in small bowl; pour over tomato mixture and toss to coat. Season caponata to taste with salt and pepper. DO AHEAD: Caponata can be prepared 2 hours ahead. Let stand at room temperature. Prepare barbecue (medium-high heat). Peel eggplant lengthwise to create alternating 2-inch-wide intervals of peeled and unpeeled skin. Cut eggplant crosswise into 6 slices, each about 1 inch thick. Brush eggplant slices with oil; sprinkle with salt and pepper. Grill eggplant slices until slightly charred and very tender when pierced with knife, about 8 minutes per side. Place 1 grilled eggplant slice on each of 6 plates. Spoon caponata over, garnish with oregano sprigs, and serve warm or at room temperature.