Mix first 4 ingredients; pour into a Ziploc bag and add chicken breasts. Marinate for at least 1 hour. Grill marinated chicken and slice into 1/2" strips.
Slice cabbage, finely chop celery; finely slice green onions on the bias. Chop cashews and toast lightly in a dry skillet; set aside. Whisk all dressing ingredients in a large bowl until well combined. Toss greens and celery with dressing. Top with chicken slices, orange sections, and nuts. Garnish with sesame seeds and green onions.