Wash the chicken breasts and pat them dry with paper towels. Slice the chicken into thin strips. Place the chicken in a bowl and season with salt and black pepper.
Wash the broccoli and cut it into small florets if needed. Mince the garlic and ginger. Keep everything ready before cooking.
In a small bowl, add soy sauce, oyster sauce, cornstarch, and water. Mix well until the cornstarch fully dissolves. Set the sauce aside.
Heat olive oil in a large pan or wok over medium-high heat.
Add the sliced chicken to the hot pan. Cook for 4–5 minutes while stirring until the chicken turns white and is fully cooked.
Add the minced garlic and ginger to the pan. Stir for about 30 seconds until fragrant.
Add the broccoli florets to the pan and stir well with the chicken. Cook for 2–3 minutes.
Pour the prepared sauce into the pan. Stir everything well so the chicken and broccoli are coated evenly.
Cook for another 2 minutes until the sauce thickens and the broccoli becomes tender but still slightly crisp.
Turn off the heat and serve the chicken broccoli stir fry warm.