Heat the vegetable oil in a large skillet over medium-high heat. Add the sliced flank steak and cook for 3 to 4 minutes until browned on the outside but still slightly pink inside. Remove the beef to a plate and set aside.
Add the broccoli florets to the same skillet. Stir-fry for 3 minutes until the broccoli turns bright green and starts to soften.
Stir in the minced garlic and grated ginger. Cook for 30 seconds until fragrant.
In a small bowl, whisk together the soy sauce, brown sugar, beef broth, and cornstarch. Pour the mixture into the skillet with the broccoli.
Return the beef to the skillet. Stir everything together and cook for 2 to 3 minutes until the sauce thickens and coats the beef and broccoli evenly.
Spoon the stir-fry over the cooked white rice and sprinkle with sesame seeds before serving.