Bring a pot of water to a boil. Add the broccoli florets and blanch for 2 minutes. Remove and set aside.
Heat a large pan or wok over medium heat and add cooking oil. Add the minced garlic and ginger, stirring until fragrant.
Add the thinly sliced chicken breast to the pan, stir-frying until it’s almost cooked through.
Pour in the soy sauce and oyster sauce, and let the chicken simmer for a couple of minutes. Add the black pepper powder and brown sugar, stirring well.
Stir the cornstarch mixture well, then pour it into the pan. Let the sauce come to a gentle boil, stirring until it thickens.
Return the blanched broccoli to the pan and let everything simmer for 1-2 minutes, allowing the flavors to blend.
Turn off the heat, drizzle with sesame oil, and give it a final toss.
Serve hot, and enjoy this delicious, saucy chicken broccoli stir-fry!