In a bowl, mix soy sauce, oyster sauce, sesame oil, cornstarch, sugar, and chicken broth to make the sauce. Set aside.
Heat 1 tbsp vegetable oil in a wok or large skillet over high heat. Add chicken and stir-fry until cooked through, about 4-5 minutes. Remove and set aside.
Add remaining oil to the wok. Stir-fry garlic and ginger for 30 seconds until fragrant. Add broccoli and stir-fry for 2-3 minutes until bright green.
Return chicken to the wok. Pour in the sauce and stir well. Cook for another 2 minutes until the sauce thickens.
Garnish with red pepper flakes if desired and serve hot over rice.