Place peach cores in a medium saucepan, add vinegar, basil stalks and enough water to just cover cores, this
Place over low heat and cook, stirring occasionally, for 1 hour 30 minutes for flavours to develop.
Strain, reserving liquid and cores separately. Return liquid to pan over high heat, bring to the boil and cook for 10 minutes or until reduced by half.
Heat a chargrill pan or barbecue on high.
Grill peach meat, skin-side down, for 3 minutes or until blackened.
Cut cheeks into thirds and toss with reduced peach juices and basil leaves.
Top with bocconcini and edible flowers, if using, and drizzle with oil to serve.