Cut peaches in half and remove pits. Cut peach halves into wedges. Coat with olive oil and place flesh side down on heated medium-high grill for 1-2 minutes (you can also use a grill pan on the stove). Turn over for another 1-2 minutes. Set peach wedges aside.
Put a dollop of burrata on the plate and arrange peach wedges on top. Drizzle honey over peaches and burrata and garnish with mint leaves. If you like a savory kick, sprinkle a small pinch of sea salt.