In a bowl, combine soy sauce, water, brown sugar, cornstarch, garlic, and ginger. Add the thinly sliced beef and toss to coat. Let marinate for 15 minutes.
Heat vegetable oil in a large skillet over medium-high heat. Add marinated beef and cook until browned and nearly cooked through, about 3-4 minutes.
Add the steamed broccoli and the remaining marinade. Cook, stirring frequently, until the sauce thickens and coats the beef and broccoli, about 2-3 minutes.