Toss sliced chicken with 1 tbsp soy sauce and 1 tsp cornstarch. Set aside.
- Heat olive oil in a large skillet or wok over medium-high heat. Add chicken and stir-fry until golden and cooked through, about 5–6 minutes. Remove from pan and set aside.
- In the same pan, add a bit more oil if needed. Sauté garlic and ginger for 30 seconds until fragrant.
- Add broccoli and stir-fry for 3–4 minutes until bright green and tender-crisp.
- In a small bowl, whisk together remaining soy sauce, oyster sauce (if using), chicken broth, cornstarch, and sesame oil.
- Pour sauce into the pan and stir until thickened, about 1–2 minutes.
- Return chicken to the pan and toss everything together until coated and heated through.
- Garnish with green onions and sesame seeds before serving.