Slice the beef against the grain into 0.5 cm thick slices and transfer to a bowl.
Add soy sauce, peanut oil, and cornstarch. Mix well and let marinate for 10 minutes.
Combine all sauce ingredients in a bowl and mix well. Set aside.
In a nonstick skillet, add water and heat until boiling. Add broccoli and cover to steam for about 1 minute.
Transfer broccoli to a plate when done.
Wipe the pan if necessary, add oil, and heat over medium-high.
Spread the steak in a single layer and cook undisturbed for 30 seconds, then flip and cook until lightly charred.
Add garlic and ginger to the pan, stirring to prevent burning.
Return broccoli to the pan, mixing everything together.
Pour the sauce into the skillet with the beef and broccoli.
Cook and stir until the sauce thickens, about 1 minute.
Serve the dish hot immediately as a main course.