Place sesame seeds in a dry non-stick skillet and heat over medium heat until fragrant, about 5 minutes.
In a medium skillet add olive oil and sesame oil, turn heat to medium-high, cook chicken cubes until cooked through and crispy, approximately 10 minutes.
In the meantime, add all dressing ingredients, whisk until combined.
Combine cooked chicken, cabbage, lettuce, and carrots in a large salad bowl. Drizzle dressing over salad mix and toss to combine. Sprinkle salad with sesame seeds.