Marinate the Beef: In a bowl, combine thinly sliced beef with 1 tbsp soy sauce, 1 tsp cornstarch, and a splash of rice wine (optional). Marinate for at least 15 minutes (or up to 30 minutes) at room temperature.
Prepare Vegetables: Wash and chop all vegetables into bite-sized pieces.
Make the Sauce: In a small bowl, whisk together the remaining 2 tbsp soy sauce, oyster sauce, chicken broth, cornstarch, minced garlic, and minced ginger. Set aside.
Stir-Fry Beef: Heat 1 tbsp of cooking oil in a wok or large skillet over high heat until shimmering. Add the marinated beef in batches (don't overcrowd) and stir-fry until browned on all sides (about 2-3 minutes per batch). Remove beef from the pan and set aside.
Stir-Fry Vegetables: Add the remaining 1 tbsp of cooking oil to the wok. Add the sliced onion, carrots, and celery and stir-fry for 2-3 minutes, until slightly tender-crisp. Add the bean sprouts and bell peppers (if using) and stir-fry for another minute.
Combine and Thicken: Return the cooked beef to the wok with the vegetables. Pour in the sauce and stir continuously until the sauce thickens and coats all the ingredients (about 1-2 minutes).
Finish and Serve: Remove from heat and drizzle with sesame oil. Garnish with sliced green onions and sesame seeds, if desired. Serve hot over steamed rice.