In a bowl, whisk together soy sauce, brown sugar, rice vinegar, sesame oil, garlic, and ginger. Add the sliced beef and marinate for at least 30 minutes, or up to 2 hours in the refrigerator for more flavor.
In a small bowl, mix cornstarch and water until smooth. Set aside.
Heat vegetable oil in a large skillet or wok over medium-high heat. Remove the beef from the marinade (reserve the marinade) and stir-fry for about 3-4 minutes until browned. Remove the beef from the skillet and set aside.
In the same skillet, add broccoli, bell pepper, and carrot. Stir-fry for 3-5 minutes until the vegetables are tender-crisp.
Return the beef to the skillet and pour in the reserved marinade. Bring to a simmer, then stir in the cornstarch mixture. Cook for another 2-3 minutes until the sauce thickens.
Serve the beef teriyaki over cooked white rice and garnish with chopped green onions.