1 12-ounce container grape or cherry tomatoes, quartered lengthwise
2 celery stalks, finely diced
1/2 cup chopped Vidalia or Maui onion
5 large green olives, pitted, thinly sliced (about 2 tablespoons)
2 tablespoons coarsely chopped fresh oregano plus sprigs for garnish (woops, we forgot this)
1 tablespoon drained capers, rinsed
1 garlic clove, minced
Pinch of dried crushed red pepper
3 tablespoons red wine vinegar
1 tablespoon extra-virgin olive oil plus additional for brushing
1 large eggplant (1 1/2 to 13/4 pounds), trimmed
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. (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 one grilled eggplant slice on each of six plates. Spoon caponata over, garnish with oregano sprigs, and serve warm or at room temperature.