In a small bowl, whisk together the soy sauce, oyster sauce, and cornstarch mixture. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over high heat. Add the thinly sliced beef in a single layer and cook for 2-3 minutes until browned. Remove the beef to a plate and set aside.
In the same skillet, add the remaining 1 tablespoon of oil. Add the broccoli florets and stir-fry for 3-4 minutes until bright green and slightly tender.
Add the minced garlic and ginger to the skillet with the broccoli. Stir-fry for 1 minute until fragrant.
Return the beef to the skillet and pour in the prepared sauce mixture. Stir everything together and cook for 2-3 minutes until the sauce thickens and coats the beef and broccoli.
Drizzle with sesame oil (if using) and give it a final stir.
Serve hot over cooked rice. Enjoy your flavorful beef and broccoli stir-fry!