Whisk the water, soy sauce, brown sugar and cornstarch together in a small bowl until smooth.
Heat half of the oil in a large skillet over medium-high heat. Add half of the beef in a single layer and sear for 1–2 minutes per side, until browned. Move it to a plate and repeat with the remaining oil and beef.
Reduce the heat to medium. Add the garlic and ginger to the skillet and stir for 30 seconds.
Add the broccoli. Whisk the sauce again and pour it in. Cover and simmer for 3–4 minutes, until the broccoli is bright green and crisp-tender.
Return the beef and any juices to the skillet. Simmer uncovered for 1–2 minutes, stirring, until the sauce is thick and glossy.
Serve over rice.