Melt the butter in a medium saucepan. Browning the butter will add more depth to the flavor, but if that sounds intimidating, just melt it! *See my tips for more info about browning butter.
Add the rest of the sauce ingredients to the melted butter & stir frequently until sauce comes to a slow boil and thickens. You want your peaches to be tender, but not soggy. They should not need to cook for more than a few minutes. Once your sauce has thickened, turn off your stove, and remove the pan from the heat.
Allow the sauce to cool for 5 or so minutes and use immediately or store it in an airtight container in the fridge for a couple days.