In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the minced garlic and ginger, sautéing for about 30 seconds until fragrant.
Add the ground beef to the skillet, breaking it apart with a spatula. Cook until browned and fully cooked, about 5-7 minutes. Drain excess fat if necessary.
Stir in the broccoli florets and cook for an additional 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.
Stir to combine and cook for another 2-3 minutes 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.