In a bowl, combine the soy sauce, sesame oil, ginger, garlic, brown sugar, rice vinegar, and cornstarch. Whisk until well mixed.
Add the sliced flank steak to the marinade, ensuring all pieces are coated. Let it marinate for at least 30 minutes, or up to 2 hours in the refrigerator for more flavor.
Heat vegetable oil in a large skillet or wok over medium-high heat. Add the marinated beef in a single layer and cook for about 2-3 minutes until browned. Remove the beef and set aside.
In the same skillet, add the bell pepper and broccoli. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Return the beef to the skillet, add the green onions, and stir everything together. Cook for an additional 2 minutes to heat through.
Sprinkle with sesame seeds before serving. Serve over cooked rice.