In a medium bowl, combine beef strips with soy sauce, cornstarch, and sesame oil; mix well to coat. Let the beef marinate for at least 15 minutes at room temperature, or refrigerate for up to 30 minutes.

In a separate small bowl, whisk together beef broth, soy sauce, oyster sauce, brown sugar, cornstarch, minced garlic, and grated ginger until smooth. Set aside.

Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the broccoli florets and stir-fry for 3-5 minutes until tender-crisp. Remove broccoli from the skillet and set aside.

Add the remaining 1 tablespoon of vegetable oil to the skillet. Once hot, add the marinated beef in a single layer and cook for 2-3 minutes per side, until browned and cooked through. Avoid overcrowding the pan; cook in batches if necessary.

Return the cooked broccoli to the skillet with the beef. Pour the prepared sauce over the beef and broccoli. Cook, stirring constantly, for 1-2 minutes, or until the sauce has thickened and coats the beef and broccoli evenly. Serve immediately over hot cooked rice, garnished with sesame seeds and sliced green onions if desired.