Slice the flat iron steak thinly against the grain, about ⅛–¼ inch thick. For easier slicing, optionally place it in the freezer for 15–20 minutes first. Toss the sliced beef with the marinade's soy sauce, cornstarch, and oil. Let marinate for 10–15 minutes while preparing the remaining ingredients.

Whisk together the broth, sauce's soy sauce, brown sugar, cornstarch, garlic, ginger, and optional sesame oil. Set aside.

Add ½ cup water to a large skillet and bring to a simmer. Add the broccoli, cover, and steam for 2–3 minutes, until bright green and just tender. Drain the broccoli and wipe the skillet dry.

Heat 1 tablespoon cooking oil in the skillet over medium-high heat. Add half the beef in a single layer. Sear for about 1 minute, then flip and cook for another 30–60 seconds. Transfer to a plate. Repeat with the remaining tablespoon oil and beef. These timings are approximate and depend on slice thickness and pan heat.

Whisk the sauce again to redistribute the cornstarch, then pour it into the skillet. Bring to a simmer and stir for 1–2 minutes, until thickened. If too thick, add a small splash of broth or water.

Return the broccoli, beef, and any accumulated juices to the skillet. Toss briefly until coated and the beef is cooked through. Serve immediately with rice or fried rice.