Heat the sesame oil on medium heat. Once hot add the chicken and carrot. Cook until the chicken is firm and cooked through. Drain off any excess liquid.
In a small bowl, combine all ingredients except sesame seeds and green onion. Whisk until smooth and pour over the cooked chicken. Bring to a simmer and cook for 1 minute, or until thick and chicken is coated. Stir in the sesame seeds. Remove from heat and top with green onion. Serve over brown rice or quinoa, if desired.