In a small bowl, whisk together soy sauce, brown sugar, cornstarch, beef broth, and sesame oil. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced beef and cook for about 3-4 minutes until browned. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add minced garlic and grated ginger, and sauté for about 30 seconds until fragrant.
Add the broccoli florets to the skillet and stir-fry for 2-3 minutes until they are bright green and tender-crisp.
Return the beef to the skillet and pour the sauce mixture over the beef and broccoli. Stir well to combine and cook for an additional 2-3 minutes until the sauce thickens.
If desired, sprinkle with red pepper flakes for added heat. Serve immediately over cooked rice.