Place all the ingredients except for the butter in a medium-sized stock pot and bring to a boil. Reduce the heat to medium-low, cover and simmer 25 minutes, stirring occasionally, until the peaches are soft.
Use an immersion blender or transfer to a blender and puree until smooth. Add the butter and stir until melted. If the sauce is too thick, add a little water to thin it out.
Store in an airtight container in the fridge for up to a week.
FOR CANNING: You can also can this sauce for long-term storage. Omit the butter and ladle the hot sauce into sterilized jars, leaving 1/2 inch headspace, wipe the rims with a damp cloth and screw on the lids/rims. Process in a boiling water canner for 10 minutes. Carefully remove the jars and let them sit undisturbed for 24 hours. Check the seals. Stored in a dark, cool place, this will keep for at least a year but for best flavor use within 6 months.