Bring first 5 ingredients to a boil over medium-high heat; cook, whisking constantly, until mixture is reduced to 1 tablespoon. Remove from heat; whisk in 1 tablespoon water and next 3 ingredients. Remove from heat; whisk in 1 tablespoon water and next 3 ingredients.
Cook over low heat, whisking constantly, 4 minutes or until slightly thickened. Remove from heat; add butter in a slow, steady stream, whisking constantly until thickened.
Pour sauce through a wire-mesh strainer into a bowl, discarding solids; stir in green onion. Serve warm.