Preheat oven to 425. Add cubed bread onto a baking sheet and toss with 2 tablespoons of olive oil and a big pinch of salt. Bake for 10 minutes, toss then bake another 5 minutes until the bread is golden and toasted. They will continue to crisp up once removed from the oven.
Make the vinaigrette. In a small bowl, add shallots, garlic, 4 tablespoons olive oil, white wine vinegar, and honey, and whisk to combine. Add salt and pepper to taste. Pour half of the dressing over the bread and toss to just soften.
Preheat grill to medium-high. In a medium sized bowl, add sliced peaches, 1 tablespoon of olive oil and a sprinkle of salt, and toss together. Place peaches son the grill and cook 1-2 minutes on each side.
Plate up. To a large plate or serving platter, add crisp salad greens, soaked bread, and torn prosciutto. Arrange peaches and burrata on top, and finish with basil, salt, pepper, and a bit more vinaigrette.