In a medium bowl, combine the chicken pieces, soy sauce, and cornstarch. Mix well and let marinate for 15 minutes.
Heat the vegetable oil in a large skillet 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 sliced onion and mushrooms. Sauté for 4-5 minutes until the vegetables are tender. Add the minced garlic and cook for an additional 1 minute.
Return the chicken to the skillet. Stir in the black pepper, sugar, and chicken broth. Bring to a simmer and cook for another 3-4 minutes until the sauce thickens slightly.
Serve the black pepper chicken over cooked rice and garnish with chopped green onions.