In a large bowl, combine the sliced flank steak with soy sauce, brown sugar, and cornstarch. Mix well and let it marinate for about 10 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated beef and stir-fry for 3-4 minutes until browned. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the onion, red bell pepper, and broccoli. Stir-fry for about 5 minutes until the vegetables are tender-crisp.
Add the minced garlic and ginger to the skillet and stir-fry for an additional 1 minute until fragrant.
Return the beef to the skillet. In a small bowl, mix the water and sesame oil, then pour it over the beef and vegetables. Stir everything together and cook for another 2-3 minutes until heated through and the sauce thickens slightly.
Serve immediately over cooked rice or noodles.