Place chopped tomatoes in a colander set over your servings bowl and season with 2 teaspoons of kosher salt. Toss to coat.
Set the tomatoes aside at room temperature to drain, tossing occasionally, while you toast the bread. Drain for a minimum of 15 minutes.
Meanwhile, preheat the oven to 350°F and adjust the rack to the center position.
On a baking sheet, toss bread cubes with 2 tablespoons of olive oil. Bake for about 15 minutes, until crisp and firm but not browned. Remove from oven and let cool.
Remove colander with tomatoes from the bowl with tomato juice.
Place colander with tomatoes on a plate.
Add garlic, mustard, vinegar, salt, and pepper to the bowl with the tomato juice. Whisking constantly, drizzle in the remaining 1/4 cup olive oil.
Add the toasted bread, tomatoes, and red onions. Add 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.