In a small bowl, whisk together the soy sauce, oyster sauce, brown sugar, sesame oil, cornstarch, and beef broth until smooth.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced beef in a single layer and cook for 2 to 3 minutes until browned. Transfer the beef to a plate.
Add the remaining tablespoon of oil to the skillet.
Stir-fry the broccoli for 3 to 4 minutes until crisp-tender.
Add the garlic and ginger, cooking for about 30 seconds until fragrant.
Return the beef to the skillet.
Pour the sauce over the beef and broccoli, stirring to coat everything evenly.
Cook for another 2 to 3 minutes until the sauce thickens and the beef is cooked through.
Garnish with green onions and sesame seeds before serving.