Prepare the chicken by shredding it into bite-sized pieces. If using raw chicken, boil or grill until fully cooked, then let cool before shredding.
Make the dressing by combining sesame oil, soy sauce, rice vinegar, and honey in a small bowl. Whisk until well blended.
In a large bowl, combine the shredded chicken, mixed salad greens, red cabbage, and carrots. Toss gently to mix.
Add the dried cranberries and sliced almonds. Drizzle the sesame dressing over the salad and toss gently again. Season with salt and pepper to taste and garnish with chopped green onions.