Preheat oven to 350 degrees F. Lightly grease a 12-cup muffin tin. Melt butter in a saucepan over low heat and set aside. Mix flour, baking powder and salt in medium bowl. In another bowl, whisk the egg, then add the sugar. Whisk until thick and thoroughly mixed. Continue to whisk, adding the milk and melted butter. Add the sour cream and stir to combine. Fold the egg mixture into the flour mixture until well combined. Add the chopped peaches and stir until just combined.
Drop tablespoons of the batter into the muffin tins until half full. Bake for 35 minutes or until a toothpick inserted into a muffin comes out clean. Cool muffins in tins for 10 minutes, then turn them out onto a wire rack to finish cooling. Serve immediately or store in an airtight container for up to 2 days.