To prepare dressing: combine all ingredients except the oils and whisk well to combine. Slowly whisk oils into dressing until combined. Set aside.
In a medium, deep skillet or a large saucepan, bring chicken stock or enough water to cover chicken to a simmer. If stock does not cover chicken, add water to cover. Add chicken and simmer for 10 to 12 minutes, depending on size or until just tender.
Cool chicken in liquid. Drain chicken and shred by tearing meat into long thing pieces (or slice with knife, if desired). Reserve in a medium serving bowl.
To toast sesame seeds, place in dry medium skillet over high heat. Shake until seeds turn light brown, about 2 minutes. Remove immediately from skillet. Reserve.
Add cucumber, green onions, and one tablespoon cilantro to bowl with chicken meat. Add dressing and mix well. Taste for seasoning. Garnish with sesame seeds and remaining cilantro.
Ingredients for the salad:
Ingredients for dressing:
