**Prepare the Chicken:** Thinly slice the chicken breast and place it in a bowl. Season lightly with salt and pepper.

**Mix the Sauce:** In a small bowl, whisk together the soy sauce, oyster sauce, hoisin sauce, cornstarch, brown sugar, chicken broth, and sesame oil. Set aside.

**Blanch the Broccoli:** Bring a pot of water to a boil. Add the broccoli florets and cook for 2 minutes. Drain and immediately transfer the broccoli to a bowl of ice water to stop the cooking process. Drain and set aside.

**Cook the Chicken:** Heat 1 tbsp of vegetable oil in a wok or large skillet over medium-high heat. Add the sliced chicken and stir-fry until lightly browned and cooked through, about 4-5 minutes. Remove the chicken from the wok and set aside.

**Sauté Garlic and Ginger:** In the same wok, add the remaining 1 tbsp of vegetable oil. Sauté the minced garlic and grated ginger until fragrant, about 30 seconds.

**Combine and Cook:** Return the chicken to the wok, add the blanched broccoli, and pour the sauce over the top. Stir well to coat all ingredients evenly. Cook for 2-3 minutes, or until the sauce thickens and everything is heated through.

**Serve:** Remove from heat and serve the chicken and broccoli over steamed rice or noodles.