Marinate the Beef: In a medium bowl, toss the thinly sliced beef with 1 tablespoon of soy sauce and the cornstarch. Mix until the beef is evenly coated.
Prepare the Sauce: In a small bowl, combine the remaining 1 tablespoon of soy sauce, oyster sauce, and chicken broth. Set aside.
Cook the Beef: Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated beef and stir-fry for 2-3 minutes, or until the beef is mostly cooked through.
Cook the Shrimp: In the same skillet, add another 1 tablespoon of vegetable oil. Add the shrimp and stir-fry for 1-2 minutes, or until they turn pink and opaque. Remove the shrimp from the skillet and set aside with the beef.
Stir-Fry the Vegetables: In the same skillet, add a little more oil if needed. Incorporate the sliced onion, bell pepper, and carrots into the pan. Stir-fry for approximately 3-4 minutes, or until the vegetables begin to become tender. Add the broccoli florets, minced garlic, and ginger, and continue to stir-fry for another 2 minutes.
Combine and Cook: Return the cooked beef and shrimp to the skillet. Drizzle the sauce mixture over the stir-fry and toss everything together to ensure an even coating. Add the bean sprouts and bamboo shoots (if using) and stir-fry for an additional 1-2 minutes, until everything is heated through and well combined.
Finish and Serve: Drizzle with sesame oil, if using, and season with salt and pepper to taste. Serve the Beef and Shrimp Chop Suey hot over steamed rice or noodles.