1. Preheat grill to medium-high. (Alternatively, heat a grill pan over mediumhigh heat until hot.) Using 3 tablespoons of oil, brush bread slices on both sides.

2. Grill bread slices, turning once, until toasted on both sides, about 5 minutes total. Rub both sides with halved garlic. Tear into bite-size pieces.

3. Toss bread, tomatoes, onion, bocconcini, and sliced basil in a serving bowl.

4. Whisk together vinegar and minced garlic in a small bowl. Whisking constantly, pour in remaining 6 tablespoons oil in a slow, steady stream, and whisk until emulsified. Pour over salad. Season with salt and pepper. Let stand at room temperature, tossing occasionally, 1 hour. Garnish with whole basil leaves.