To make the salad: Preheat the oven to 400°. Oil a baking sheet.
Put the cornbread on the prepared baking sheet, drizzle with olive oil, and season with salt. Bake until nicely toasted, about 15 minutes. Let cool completely.
In a large salad bowl, combine the cornbread, peppers, cucumber, tomatoes, onion, and basil.
To make the dressing: In a small bowl, whisk all the ingredients together.
Add the dressing to the cornbread and vegetables, and toss. Let stand at room temperature for about 20 minutes before serving.