In a large mixing bowl, toss the cubed bread with enough extra-virgin olive oil to coat liberally, and season with salt and pepper. Arrange the bread cubes in an even layer on one side of a large baking sheet. In the same mixing bowl, toss the diced peppers with some extra-virgin olive oil, salt and pepper and place them on the other side of the baking sheet. Place the baking sheet into the oven to bake until the bread is crispy and golden brown and the peppers have softened, 10 to 12 minutes. Keep an eye on it so the bread doesn't burn!
Meanwhile, make the vinaigrette. In a small mixing bowl, combine the vinegar, mustard and garlic. Slowly drizzle in the olive oil while whisking. Season the vinaigrette with salt and pepper.
Once the bread is toasted, combine the bread and peppers with the smoked mozzarella, snap peas and tomatoes (you can use the same bowl you tossed the bread and peppers in). Toss the salad with the vinaigrette and add the torn basil leaves. Let stand for 10 minutes before serving to allow the flavors to develop.