Roasted-Vegetable Panzanella

Arrange oven racks in upper and lower thirds of oven and preheat oven to 425°F.
Mince and mash garlic to a paste with a pinch of salt using a large heavy knife, then transfer to a small bowl and add 1/2 cup olive oil in a slow stream, whisking until combined well. Put bread cubes in a large bowl and drizzle with 3 tablespoons garlic oil, tossing to combine, then divide bread between 2 large shallow baking pans, arranging in 1 layer. Toast in oven, stirring once or twice, until golden, 10 to 12 minutes. Leave oven on.
Gently toss tomatoes with 1 tablespoon oil (not garlic oil), 1/4 teaspoon salt, and 1/8 teaspoon pepper in a bowl, then arrange in 1 layer on a large shallow baking pan. Toss green beans in same bowl with remaining 2 tablespoons oil and 1/4 teaspoon salt and 1/8 teaspoon pepper, then arrange in 1 layer in another large shallow baking pan. Roast vegetables, switching position of pans halfway through roasting and shaking pans once or twice, until tomatoes are very tender but not falling apart and beans are just tender and browned in spots, 12 to 16 minutes. Cool vegetables in pans until ready to assemble salad.
While vegetables roast, add vinegar to remaining garlic oil along with capers, sugar, remaining 1/2 teaspoon salt, and 1/4 teaspoon pepper and whisk to combine well.
Put green beans, tomatoes (along with any pan juices), toasted bread, beans, mozzarella, and basil in a large bowl, then drizzle with dressing and stir to combine well. Let stand 10 to 15 minutes at room temperature to allow flavors to develop, then stir just before serving.