Combine half & half, Dijon mustard, flour and salt in 1-quart saucepan. Cook over medium heat, stirring constantly, until mixture begins to thickened (3 to 5 minutes). (DO NOT BOIL.)
Stir in green onions; remove from heat. Add butter, stirring constantly with wire whisk, until smooth.
Serve sauce immediately over chicken breasts or fish.
Add additional 1 tablespoon flour, if thicker sauce is desired.