To grill peaches: Split peaches in half, place them into a bowl. Drizzle peaches with olive oil, season lightly with salt and freshly ground black pepper. Grill for 5 minutes or until soft and grilled marks are seen. Let cool, dice peaches into 1-inch pieces. Set aside.
To roast tomatoes: Preheat oven to 350 F. Drizzle baking dish with olive oil lightly, scatter tomatoes on top. Season with salt and freshly ground black pepper. Bake for 15 minutes. Set aside.
To make croutons: Cut bread slices into 1½-inches cubes, place them on baking sheet, and drizzle with lemon juice lightly, season with sea salt. Bake for 10 minutes in the oven or until golden and light.
To make panzanella: On a large platter, transfer diced peaches; scatter tomatoes and croutons on top. Place sporadically sliced onion. Tear burrata cheese into bite-size pieces with your fingers and place sporadically on top of the salad. Drizzle with extra-virgin olive oil and aged balsamic vinegar. Season with black lava sea salt on top. Scatter mint and basil leaves on top.