In a bowl, combine the chicken pieces with soy sauce, cornstarch, black pepper, and a pinch of salt. Mix well and let marinate for at least 15 minutes.
Heat vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the garlic, ginger, onion, bell pepper, and mushrooms. Stir-fry for about 3-4 minutes until the vegetables are tender.
Return the chicken to the skillet and pour in the chicken broth and sesame oil. Stir everything together and cook for an additional 2-3 minutes, allowing the flavors to meld.
Taste and adjust seasoning if necessary. Serve hot, garnished with chopped green onions.