(Optional) For grilled peaches: Melt butter with brown sugar and cinnamon, then brush over peach halves. Grill peaches cut-side down for 4–6 minutes until caramelized. Let cool.
In a cast iron skillet or saucepan, combine chopped peaches, brown sugar, and cinnamon.
Cook over medium heat (either on the stovetop or grill) for 5–8 minutes, until the peaches are soft and the sugar has melted.
Transfer to a blender with ½ cup water and blend until smooth.
Strain the syrup into a container, then stir in a splash of vanilla extract. Let cool before using.