Combine sliced chicken with soy sauce, sherry, and black pepper in a bowl. Mix all the ingredients. Marinate for 10 minutes.
Combine water (or chicken broth) with oyster sauce and cornstarch. Stir until the cornstarch is completely diluted. Set this aside for now.
Heat the oil in a wok or wide frying pan.
Add the minced garlic. Sauté until it starts to get light brown.
Stir fry the marinated chicken. You can pour the remaining marinade on the wok. Cook in high heat while stirring until the chicken turns light to medium brown. Ensure that the garlic does not get burnt in the process. Otherwise, you will need to adjust the heat to medium or lower and continue to cook until the chicken gets that nice color.
Add the broccoli florets. Stir fry for 1 minute if you are using steamed frozen broccoli. Add another minute if using fresh broccoli florets.
Pour the bowl that contains the mixture of oyster sauce, water, and cornstarch. You may want to stir it one more time before pouring to be sure. Stir and cook until the sauce reduces in half or reaches your desired thickness.
Enjoy over a bowl of warm rice.