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Whisk together the rice wine vinegar with the toasted sesame oil. If you have regular sesame oil on hand, go ahead and use it, the toasted variety just gives a little more depth of flavor.
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Whisk in the green gar until it is dissolved, then add the soy sauce, chopped green onions, the vegetable oil and the dried spices. Lastly add the minced garlic and the fresh cilantro. Pour half of this mixture into a separate container and reserve for the salad dressing.
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Pour the remaining half of the mixture over the boneless skinless chicken breasts and refrigerate them for at least 1 hour, or up to 4 hours.
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Preheat the oven to 350F. Remove the chicken breasts from the marinade and place them in a glass or ceramic baking dish. Discard the remaining marinade and cover the baking dish with foil.
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Bake the marinated chicken breasts in the preheated oven for about 45 minutes, until the chicken is no longer pink in the center and an instant read thermometer reads 175F. If the chicken isn't quite cooked and you are running short on time, carefully slice them horizontally through the center and layer them in the baking dish, re-cover it and finish the baking.
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When the chicken breasts are cooked, set them aside to cool. When they are cool enough to handle, either shred the meat or slice the breasts into thin julienned strips.
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Assemble the salad: Combine the shredded cabbages, carrots and chopped green onions. Toss in the cooled chicken pieces. Add the reserved dressing and toss well. Garnish with the toasted almond slivers and chopped cilantro.