Place the sliced peaches in a mixing bowl or on a small baking sheet. Lightly drizzle with avocado oil. Season with S&P as desired. Toss to coat.
Place the peaches directly on the grill grates. Grill 3-4 minutes per side, or until nicely charred & slightly softened. Transfer the grilled peaches to a plate or small baking sheet.
Arrange the grilled peaches on a large plate or serving platter. Gently tear the prosciutto & burrata over the peaches. Finish with the basil, a quick drizzle of olive oil & white balsamic, & a good pinch of flaky sea salt & ground black pepper.