Combine sake and rice vinegar with scallion and cilantro in small saute pan over medium-high heat. Bring to a medium boil and let boil until approximately 1 Tbsp of liquid remains. Strain sake liquid. Place matcha powder in medium bowl and whisk in sake liquid until evenly combined and frothy. Transfer matcha sake liquid back to saute pan and reduce heat to low. Add butter, a few small cubes at a time, while whisking continuously to create an emulsion. Season with salt and white pepper to taste. Keep warm for use, or sauce will begin to break.
PRO TIP: Butter must be cold in order to create an emulsion. Warm butter will melt too quickly and break in the sauce, separating into globules of fat and liquid.