In a small bowl, mix the low sodium soy sauce, oyster sauce, cornstarch, and water until smooth. Set aside.
Heat olive oil in a large skillet or wok over medium-high heat.
Add the minced garlic and grated ginger to the skillet and sauté for 1 minute until fragrant.
Add the sliced chicken breast to the skillet and cook for 5-6 minutes, stirring occasionally, until the chicken is cooked through and no longer pink.
Add the broccoli florets to the skillet and stir-fry for 4-5 minutes until the broccoli is tender-crisp.
Pour the sauce mixture over the chicken and broccoli, stirring well to coat evenly.
Cook for an additional 2-3 minutes until the sauce thickens and coats the ingredients.
Season with black pepper and crushed red pepper flakes, stirring to combine.
Remove from heat and serve immediately.