For the cornbread: Preheat the oven to 400 degrees F. Oil a baking sheet.
Put the cornbread on the prepared baking sheet, drizzle with oil and season with salt. Bake until nicely toasted, about 15 minutes. Let cool completely.
For the dressing: Whisk the mustard, vinegar, oil, capers, salt and pepper together in a large bowl.
For the salad: Add the peaches, cucumbers, tomatoes and onions to the dressing and toss. Add in the cornbread cubes and basil and toss again. Let stand at room temperature for about 20 minutes before serving.
Drizzle olive oil over the top. Place slices of prosciutto over the top.