In a small bowl, whisk together soy sauce, oyster sauce, 1 tablespoon cornstarch, beef broth, brown sugar, and sesame oil. Set aside.
In a medium bowl, toss sliced steak with the remaining tablespoon of cornstarch until coated.
Heat 1 tablespoon vegetable oil in a large skillet or wok over medium-high heat. Add the steak and cook for 2-3 minutes until browned. Remove from the skillet and set aside.
Add the remaining tablespoon of oil to the skillet. Stir in garlic, ginger, and broccoli, cooking for 2-3 minutes until broccoli is bright green and slightly tender.
Return the beef to the skillet and pour in the prepared sauce. Stir-fry for 2-3 minutes until the sauce thickens and everything is well coated.
Serve hot over cooked white rice.