Place chopped tomatoes in a colander set over a bowl and season with salt. Drain for a minimum of 15 minutes.
Meanwhile, preheat oven to 350°F.
In a large bowl, toss bread cubes with 2 tablespoons olive oil. Transfer to a sheet pan. Bake about 15 minutes, until crisp and firm but not browned. Remove from oven and let cool.
Remove colander with tomatoes from bowl with tomato juice. Place colander with tomatoes in sink. Add garlic, mustard, and vinegar to bowl with tomato juice. Whisking constantly, drizzle in remaining 1/2 cup olive oil. Season dressing to taste with salt and pepper.
Combine toasted bread, tomatoes, onion, cucumbers and dressing in a large bowl. Add mozzarella and basil leaves. Toss everything to coat and season with salt and pepper.
Let rest 30 minutes before serving, tossing occasionally until the dressing is absorbed by the bread.