In a small bowl, mix soy sauce, oyster sauce, hoisin sauce, cornstarch, and chicken broth. Set aside.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add chicken, season with salt and pepper, and cook until browned. Remove and set aside.
Add the remaining oil, garlic, and ginger. Stir-fry for 30 seconds.
Add broccoli and stir-fry for 3-4 minutes until tender-crisp.
Return chicken to the skillet, pour in the sauce mixture, and toss everything together. Cook for another 2-3 minutes until sauce thickens.
Serve hot with rice or noodles. Garnish with sesame seeds if desired.