In a small saucepan, combine shallot or green onion, wine and vinegar.
Cook until liquid reduces to about 1 tablespoon.
Strain liquid into a medium saucepan.
Discard shallot or green onion.
Over low heat, whisk in butter, one piece at a time, until sauce is thick and creamy.
Whisk constantly, removing from heat occasionally to prevent separation.
Season with salt and white pepper to taste.
If necessary, sauce can be held until serving by placing pan in a container of warm, not simmering, water.