Remove pits from 2 unpeeled peaches; chop. Set remaining whole peaches aside.
In a medium saucepan, combine chopped peaches, wine, 1/3 cup basil, and sugar, if necessary, to sweeten. Bring to boiling; reduce heat. Simmer, uncovered, for 12 to 15 minutes or until sauce is slightly thickened.
Remove and discard the basil. Pour peach mixture into a blender or food processor; cover and blend or process until smooth.
Remove pits from remaining peaches and cut into wedges. Serve with peach sauce and additional basil.