In a small bowl, whisk together soy sauce, brown sugar, rice vinegar, sesame oil, garlic, and ginger until well combined. Set aside.
In a large skillet or wok, heat vegetable oil over medium-high heat. Add the sliced flank steak and cook for about 3-4 minutes until browned. Remove the beef from the skillet and set aside.
In the same skillet, add bell pepper, broccoli, and snap peas. Stir-fry for about 4-5 minutes until the vegetables are tender-crisp.
Return the beef to the skillet and pour the teriyaki sauce over the mixture. Stir well to coat everything evenly and cook for an additional 2-3 minutes until the sauce thickens slightly.
Remove from heat and garnish with chopped green onions and sesame seeds if desired. Serve over cooked rice.