Make the sauce by mixing together sesame oil, chicken broth, brown sugar, soy sauce, dark soy sauce, rice vinegar, black pepper, and corn starch.
Toss the chicken with some of the sauce, salt, and more corn starch.
Heat oil in a pan and cook the chicken until browned on all sides, then remove and set aside.
In the same pan, cook the garlic and ginger for 30 seconds, then add the green peppers and onions. Cook until crisp-tender.
Add the remaining sauce to the pan and bring to a simmer. Return the chicken to the pan and toss to coat everything in the sauce.
Serve hot.
