Slice the boneless skinless chicken breasts into thin strips. In a small bowl, mix the cornstarch with the water until smooth. Set it aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced chicken to the hot pan. Cook for 4–5 minutes, stirring often, until the chicken is lightly browned.
Add the minced garlic and minced ginger. Stir and cook for about 30 seconds until fragrant.
Add the sliced bell peppers and broccoli florets. Stir-fry for 3–4 minutes until the vegetables are tender-crisp.
Pour in the soy sauce and oyster sauce. Stir well so the chicken and vegetables are evenly coated.
Pour the cornstarch mixture into the pan. Stir continuously as the sauce thickens and coats the chicken and vegetables.
Season with salt and black pepper to taste. Stir everything together and cook for another 1–2 minutes until the chicken is fully cooked and the sauce is glossy.