In a small bowl, whisk together soy sauce, brown sugar, rice vinegar, cornstarch, and water until smooth. Set aside.
Heat vegetable oil in a large skillet or wok over medium-high heat. Add the sliced flank steak and cook for about 3-4 minutes, or until browned. Remove the beef from the skillet and set aside.
In the same skillet, add broccoli, red bell pepper, and snap peas. Stir-fry for 3-5 minutes until the vegetables are tender-crisp.
Add minced garlic and grated ginger to the vegetables, stirring for about 30 seconds until fragrant.
Return the beef to the skillet and pour the sauce over the mixture. Stir well to combine and cook for an additional 2-3 minutes until the sauce thickens.
Remove from heat and garnish with sliced green onions and sesame seeds if desired. Serve hot over rice or noodles.