In a bowl, whisk together beef broth, soy sauce, cornstarch, brown sugar, and black pepper. Set aside.
Heat vegetable oil in a large skillet or wok over high heat. Add beef strips and stir-fry until browned, about 2-3 minutes. Remove beef from skillet and set aside.
Add sliced bell peppers and onion to the skillet and stir-fry until slightly tender, about 3-4 minutes. Add minced garlic and grated ginger and cook for another minute.
Pour the sauce mixture into the skillet and bring to a simmer, stirring constantly until the sauce thickens, about 1-2 minutes.
Return the beef to the skillet and toss to coat with the sauce. Cook for another minute, until heated through.
Drizzle with sesame oil (optional) and serve hot over rice or noodles.
Notes
For extra flavor, marinate the beef strips in a mixture of soy sauce, cornstarch, and sesame oil for at least 30 minutes before cooking.