In a small bowl, whisk together the soy sauce, brown sugar, cornstarch, ginger, garlic, and beef broth until the cornstarch is fully dissolved.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the broccoli florets and 2 tablespoons of water to the pan. Cover with a lid and steam for 2 minutes until tender-crisp and bright green. Remove the broccoli and set aside.
Wipe the skillet dry and add the remaining 1 tablespoon of oil. Increase heat to high.
Add the beef slices in a single layer and sear without moving for 2 minutes. Stir and cook for another 1-2 minutes until browned.
Pour the sauce mixture into the skillet with the beef. Cook, stirring constantly, for 1-2 minutes until the sauce thickens and becomes glossy.
Return the cooked broccoli to the skillet and toss to coat thoroughly with the sauce. Serve immediately.