Prepare the beef: In a small bowl, combine sliced beef with 1 tablespoon soy sauce, cornstarch, and white pepper. Let marinate for 10 minutes while preparing other ingredients.
Prepare the sauce: In another small bowl, whisk together 2 tablespoons soy sauce, oyster sauce, sesame oil, rice vinegar, and 1/4 cup water. Set aside.
Prep vegetables: Slice bell peppers and onion into strips, mince garlic and ginger, chop green onions, and cut broccoli into bite-sized florets. Pat vegetables dry to prevent excess moisture.
Heat the wok or large skillet: Heat 2 tablespoons of vegetable oil in a wok or large skillet over high heat until smoking, about 2 minutes.
Cook the beef: Working in batches to avoid overcrowding, add the marinated beef to the hot oil. Stir-fry for 2-3 minutes until browned on the outside but still slightly pink inside. Transfer to a plate.
Cook aromatic vegetables: Add remaining 1 tablespoon oil to the wok. Add minced garlic and ginger, stirring constantly for 30 seconds until fragrant.
Cook firm vegetables first: Add bell peppers, onion, and broccoli. Stir-fry for 3-4 minutes until vegetables begin to soften but remain crisp-tender.
Add remaining vegetables: Stir in snap peas and cook for another 1-2 minutes.
Combine and finish: Return the beef to the wok, pour in the prepared sauce, and add red pepper flakes if desired. Toss everything together for 1-2 minutes until the sauce coats all ingredients and everything is heated through.
Garnish and serve: Divide among serving bowls, garnish with chopped green onions and sesame seeds. Serve immediately over steamed rice or noodles.