In a medium bowl, combine the chicken pieces with soy sauce, cornstarch, and black pepper. Mix well and let marinate for about 15 minutes.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and stir-fry for about 5-7 minutes, or until the chicken is cooked through and lightly browned. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms and bell pepper. Stir-fry for about 3-4 minutes until the vegetables are tender.
Add the minced garlic and ginger to the skillet, cooking for an additional 1 minute until fragrant.
Return the chicken to the skillet. Pour in the chicken broth and honey (if using), stirring to combine. Cook for another 2-3 minutes until everything is heated through and the sauce thickens slightly.
Serve the black pepper chicken over cooked rice or noodles, garnished with chopped green onions.