In a medium bowl, combine the sliced beef with 2 tablespoons of soy sauce, 1 tablespoon of cornstarch, and 1 teaspoon of sesame oil; mix well and let marinate for at least 15 minutes.

In a separate small bowl, whisk together the beef broth, 2 tablespoons of soy sauce, brown sugar, 1 tablespoon of cornstarch, minced garlic, and grated ginger for the sauce.

Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.

Add the marinated beef in a single layer and cook for 2-3 minutes per side until browned and cooked through; remove beef from the skillet and set aside.

Add the remaining 1 tablespoon of vegetable oil to the skillet, then add the broccoli florets and stir-fry for 3-5 minutes until tender-crisp, adding 1/4 cup of water if needed to help steam the broccoli.

Pour the prepared sauce into the skillet and bring to a simmer, stirring constantly until it thickens.

Return the cooked beef to the skillet with the sauce and broccoli, tossing to coat everything evenly.

Serve immediately over rice or noodles, if desired.