Pour ¼ cup soy sauce, 1 tablespoon sesame oil, 1 tablespoon of garlic, the brown sugar, water, and cornstarch over the sliced flank steak. Mix well, then let marinate in the refrigerator for at least 1 hour.
In a wok or deep skillet, cook the beef and marinade thoroughly, then set aside.
In the same pan, heat the oil over medium heat. Sauté the onion, remaining tablespoon of garlic, and broccoli until the onion is translucent. Push the cooked vegetables to the side of the pan.
Beat the eggs and pour into the empty half of the pan. Scramble the eggs and mix with the rest of the vegetables.
Add the rice, remaining 3 tablespoons of soy sauce, remaining tablespoon of sesame oil, pepper, and the cooked beef. Mix well and let the rice cook until slightly crispy.