In a bowl, mix the soy sauce, oyster sauce, cornstarch, and beef broth (or water) together until well combined. Set aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the ground beef to the skillet. Break it apart with a spoon and cook until browned, about 5-7 minutes. Drain excess fat if needed.
Add the minced garlic and grated ginger to the browned beef, stirring for about 1-2 minutes until fragrant.
Add the broccoli florets to the skillet, and stir-fry them with the beef for about 3-4 minutes until they are tender but still crisp.
Pour the sauce mixture over the beef and broccoli in the skillet, stirring to coat everything evenly. Cook for an additional 2-3 minutes until the sauce thickens.
Taste and adjust seasoning with salt and pepper if needed.
Serve hot over cooked rice, and garnish with sliced green onions.