Preheat the oven to 325 degrees F. Arrange the bread cubes on a rimmed baking sheet in a single layer. Bake until dried out but not toasted, 10 to 15 minutes. Cool.
Meanwhile, put the tomatoes in a colander and toss them with 1 teaspoon salt. Let stand 20 minutes, discard any juices that drain out.
Whisk the olive oil and vinegar together in a large bowl. Add the bread, tomatoes, onion, and basil and toss to coat thoroughly. Season with salt and pepper and serve immediately.