In a medium bowl, combine the sliced beef with 1 tablespoon of soy sauce and the cornstarch. Toss to coat evenly and set aside to marinate for 10 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over high heat. Add the beef in a single layer and cook for 2-3 minutes, stirring occasionally, until browned but not fully cooked through. Remove the beef to a plate and set aside.
In the same skillet, add the remaining 1 tablespoon of oil. Add the sliced bell pepper, broccoli, and carrots. Stir-fry for 3-4 minutes until the vegetables are crisp-tender.
Add the minced garlic, ginger, and chopped green onions to the skillet. Stir-fry for 1 minute until fragrant.
Return the beef to the skillet. Pour in the beef broth or water, the remaining 1 tablespoon of soy sauce, and hoisin sauce (if using). Stir everything together and cook for 2-3 minutes until the beef is fully cooked and the sauce thickens slightly. Season with salt and black pepper to taste.
Remove from heat and transfer to a serving platter. Garnish with sesame seeds or extra green onions if desired. Serve hot with rice or noodles and enjoy your beef stir-fry!