Place the pieces of chicken breast in a large mixing bowl, add 2 tablespoon of corn starch, and a large pinch of salt, and a pinch of pepper, stir until chicken is evenly coated. You can also place the chicken in a large zip top baggie and add in the corn starch seal the bag and toss and knead to coat the chicken.
Heat a tablespoon of sesame oil in a large skillet and place the coated chicken pieces in an even layer on the bottom of the pan. Cook over medium heat until a toasted golden crust forms. Remove the cooked chicken from the pan.
Add the remaining tablespoon of sesame oil to the pan and cook the green beans for 4-5 minutes, stirring occasionally. Then remove the beans from the pan.
Pour soy sauce into the pan, add chopped garlic, ground ginger, salt, pepper. Stir the sauce continually over medium high heat and bring to a boil (1-2 minutes).
Stir the remaining tablespoon of cornstarch with 1/4 cup of water and pour into the pan, stir and bring back to a boil. Turn the heat down to allow the sauce to simmer over low heat for a few minutes until the sauce begins to thicken.
Transfer the cooked chicken and green beans to the pan in a single layer, mix and simmer another 2-3 minutes. Then turn off the heat and leave the dish covered for another 5 minutes.
Top the cooked chicken with sesame seeds and chopped green onions.