In a large skillet or wok, heat 1 tablespoon of 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. Season with salt and pepper. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the minced garlic and ginger, and sauté for about 30 seconds until fragrant.
Add the broccoli florets to the skillet and stir-fry for about 3-4 minutes until they are bright green and tender-crisp.
In a small bowl, whisk together the soy sauce, oyster sauce, cornstarch, and beef broth until smooth. Pour this mixture over the broccoli and stir well to combine.
Return the cooked ground beef to the skillet and stir everything together. Cook for an additional 2-3 minutes until the sauce thickens and everything is heated through. Drizzle with sesame oil before serving.
Serve the stir fry over cooked rice or quinoa.