Bring sake and mirin to boil in small saucepan over medium heat. Whisk in miso and sugar until smooth, about 30 seconds. Remove pan from heat and continue to whisk until sugar is dissolved, about 1 minute. Whisk in mustard, vinegar, ginger, and sesame oil until smooth. Transfer 1/3 cup glaze to bowl for grilling; reserve remaining glaze for serving.

Makes 3/4 cup