In a large bowl, combine the chicken pieces with salt, black pepper, and cornstarch. Toss until the chicken is evenly coated.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the chicken and stir-fry for about 5-7 minutes, or until cooked through and golden brown. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced bell peppers and broccoli. Stir-fry for 3-4 minutes until the vegetables are tender-crisp.
Add the minced garlic and ginger to the skillet, and stir-fry for an additional 1 minute until fragrant.
Return the cooked chicken to the skillet. Pour in the soy sauce, oyster sauce, rice vinegar, and sesame oil. Stir well to combine and heat through for another 2-3 minutes.
Serve the black pepper chicken over cooked rice.