Heat oil in a large skillet over medium-high heat.
Add steak in a single layer and cook for 2-3 minutes per side, until browned and slightly crispy. Work in batches if needed. Transfer to a plate and tent to keep warm.
Reserve 2-3 tablespoons of oil in the skillet and discard the rest.
Reduce heat to medium. Add garlic and ginger; cook for 1 minute.
Add beef broth and scrape up any browned bits.
Add broccoli and stir. Cook for 1-2 minutes, then cover and cook until bright green and just tender.
Pour in the sauce and bring to a boil.
In a small bowl, whisk water and cornstarch. Add to the skillet and stir until the sauce thickens, about 1-2 minutes.
Return beef to the skillet and toss to coat. Cook for another 1-2 minutes, until heated through.
Garnish with green onions and sesame seeds. Serve warm.