In a bowl, combine the chicken pieces with soy sauce, oyster sauce, cornstarch, and a pinch of salt. Toss to coat well and let it marinate for about 10 minutes.
Heat the vegetable oil in a large skillet or wok over medium-high heat.
Once the oil is hot, add the marinated chicken to the skillet. Stir-fry for about 5-7 minutes or until the chicken is cooked through and browned. Remove the chicken from the skillet and set it aside.
In the same skillet, add the sliced onion and garlic. Stir-fry for about 2-3 minutes until the onion becomes translucent.
Add the sliced bell pepper and continue to stir-fry for an additional 2 minutes.
Return the cooked chicken to the skillet and add the black pepper and chicken broth. Stir well to combine and let it simmer for an additional 3-5 minutes, allowing the sauce to thicken slightly.
Taste and adjust seasoning with salt if necessary.
Garnish with chopped green onions before serving.