
Preheat your grill to 450 degrees F. Ensure your grill grates are clean and free of any other food remnants.
In a medium saucepan, combine the balsamic vinegar and cherry halves. Bring to a boil, then reduce heat and simmer for 5-10 minutes until thickened.
Brush the cut sides of each peach with melted butter and grill for 3-4 minutes cut side down. Flip and cook for an additional 3-4 minutes until softened.
Transfer peaches to a platter, drizzle with cherry balsamic sauce, and sprinkle with sliced basil. Serve as is or with vanilla ice cream.