Preheat a grill or grill pan over medium-high heat. Lightly brush your peach rounds on both sides with the olive oil.
Grill your peaches for 2-3 minutes per side or until slightly softened with some sexy grill marks. Transfer to a cutting board.
Grill or toast your bread to your desired level of toastiness.
Top each piece of toast with 2 ounces of burrata. Arrange a few peach rounds and basil leaves on top of the burrata. Drizzle with honey and sprinkle with flaky sea salt. Serve immediately.