In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the ground beef and cook until browned, breaking it apart with a spatula, about 5-7 minutes. Drain excess fat if necessary.
Add the minced garlic and ginger to the skillet and sauté for about 1 minute until fragrant.
Stir in the broccoli florets and cook for another 3-4 minutes until they are bright green and tender-crisp.
In a small bowl, whisk together the soy sauce, oyster sauce, cornstarch, beef broth, and sesame oil. Pour this mixture over the beef and broccoli in the skillet.
Cook for an additional 2-3 minutes, stirring frequently, until the sauce thickens and coats the beef and broccoli evenly. Season with salt and pepper to taste.
Serve hot over cooked rice or noodles.