In a small bowl, whisk together soy sauce, beef broth, brown sugar, cornstarch, sesame oil, and red pepper flakes.
Heat 1 tablespoon of vegetable oil in a large pan over medium-high heat.
Add steak slices and cook until browned, about 3-4 minutes. Remove from pan and set aside.
In the same pan, add another tablespoon of oil, then add garlic and ginger. Sauté for 30 seconds until fragrant.
Add broccoli florets and stir-fry for 3-4 minutes until tender-crisp.
Return the steak to the pan and pour in the sauce mixture. Stir well and cook for another 2 minutes until the sauce thickens.
Serve hot over cooked rice.