Prepare the chicken by slicing the chicken breasts into thin strips, pat them dry with a paper towel, and season lightly with salt and pepper.
In a small bowl, combine soy sauce, oyster sauce, and cornstarch, mix well until smooth and set aside.
In a large skillet or wok over medium heat, add the vegetable oil, and once hot, add broccoli florets and sauté for about 3-5 minutes, or until bright green and just tender, then remove from the skillet and set aside.
In the same skillet, add the minced garlic and grated ginger, sauté for about 30 seconds, then add the sliced chicken and cook until the chicken is no longer pink, approximately 4-6 minutes.
Return the broccoli to the skillet and pour the sauce over the chicken and broccoli, stir well to coat everything in the savory sauce, and cook for an additional 2 minutes or until the sauce has thickened slightly.
Serve your Better-Than-Takeout Chinese Chicken and Broccoli over a bed of rice or noodles.