Heat vegetable oil in a large skillet over medium heat.
Add minced garlic and ginger; sauté for about 30 seconds until fragrant.
Add ground beef to the skillet, breaking it apart with a spatula and cook until browned.
Steam the broccoli florets until bright green and tender, about 4 minutes.
Drain excess fat from the cooked beef if necessary.
Stir in soy sauce, sesame oil, salt, and pepper.
Add steamed broccoli to the beef mixture and toss gently.
Cook for another 2-3 minutes to heat through.
Serve hot, garnished with sesame seeds if desired.