Whisk together soy sauce, oyster sauce, sesame oil, cornstarch, and beef broth in a small bowl to create the sauce slurry.
Heat 1 tablespoon of vegetable oil in a wok or large skillet over high heat until it reaches its smoke point.
Add the sliced beef in batches to avoid crowding; sear until browned and just cooked through, then remove and set aside.
Add the remaining tablespoon of oil to the wok and incorporate broccoli, bell pepper, and carrot.
Stir-fry vegetables for 3 to 4 minutes until they reach a tender-crisp texture.
Add the minced garlic and grated ginger to the center of the pan and cook for 30 seconds until aromatic.
Return the cooked beef to the pan and pour the sauce mixture over the ingredients.
Continuously toss the mixture for 1 to 2 minutes until the sauce has thickened and glossily coats all components.