Soak the capers in 2 tablespoons of vinegar in a small bowl for 10 minutes. Drain.
Cut the crust off of the bread. Cut into 2-inch slices and grill, drizzling about 2 tablespoons of olive oil on both sides of the bread. Once grilled, cut or tear bread into 1 inch cubes and set aside.
Submerge the tomatoes into a large saucepan of boiling water for 10 seconds. Using a slotted spoon, transfer the tomatoes to a large bowl of ice water to cool slightly. Using a small sharp paring knife, peel off the tomato skins. Cut the tomatoes in half and scoop out the seeds. Cut the tomatoes into 1-inch cubes and set aside.
In a large bowl, whisk 2/3 cup of the olive oil, 1/4 cup of vinegar, and garlic. Season with salt and pepper, to taste. Add the bread cubes, tomatoes, and basil; toss to combine.
Transfer half of the bread mixture to a 13 by 9 by 2-inch dish.
Arrange half of the roasted peppers, drained capers, and olives over the bread mixture. Repeat layering with the remaining bread mixture, then the remaining roasted peppers, capers, and olives. Cover the salad and let stand at room temperature for flavors to blend, at least 1 hour.
Garnish with the basil sprigs and serve.