Cut cabbage, celery, carrots and green onions. Reserve half the green onions. Mix all the ingredients in a large bowl and mix.
Add the remaining ingredients in the dressing including soy sauce, aji-mirin, sesame oil, rice wine vinegar, lime juice and lime zests. Mix.
Pour the sauce on the cabbage mixture and mix until the vegetables are fully dressed.
Plate. Top remaining green onions, and both the black and white sesame seeds.
The slaw can be made ahead of time and kept in the fridge.
Top with fresh herbs you have on hand.