Start by preparing the ingredients. Wash and cut the broccoli into florets. Mince the garlic and ginger.
In a small bowl, combine the soy sauce, oyster sauce, cornstarch, and water. Stir well until the cornstarch is dissolved to create a sauce mixture. Set aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the ground beef and cook, stirring frequently, until it is browned and fully cooked, about 5-7 minutes. Drain excess fat if necessary.
Add the minced garlic and ginger to the skillet with the beef. Stir-fry for 1-2 minutes until fragrant.
Add the broccoli florets to the skillet. Stir-fry for another 3-4 minutes until the broccoli is bright green and tender-crisp.
Pour the sauce mixture over the beef and broccoli. Stir well to combine and cook for an additional 2-3 minutes, until the sauce thickens and coats the meat and vegetables.
Drizzle with sesame oil, and season with salt and pepper to taste. Remove from heat.
Serve hot over cooked rice if desired.