Season the flank steak strips with the 1/2 teaspoon ground white pepper and set aside.
In a small bowl, whisk together the 1/3 cup soy sauce (or tamari), 1/3 cup water, 1 tablespoon brown sugar, the minced garlic, the grated ginger, and the 1 tablespoon cornstarch if using. Whisk until combined and the cornstarch (if used) is dissolved. Set the sauce aside.
Heat a large nonstick skillet over high heat until hot. Add 1/2 tablespoon of the sesame oil and let it shimmer.
Add the seasoned beef to the skillet in a single layer (work in batches if needed). Cook, stirring occasionally, until the beef is just about cooked through. Transfer the beef to a plate and set aside.
Add the remaining 1/2 tablespoon sesame oil to the skillet and reduce the heat to medium-high.
Add the sliced 1/2 yellow onion and cook, stirring occasionally, until the onion is softened, about 8 minutes.
Add the blanched and well-drained broccoli florets to the skillet and cook for 1 minute, stirring to combine.
Pour the reserved sauce into the skillet and stir to coat the vegetables. Bring the sauce to a simmer and cook until it thickens slightly (if you used cornstarch) or reduces slightly, about 1–2 minutes.
Return the beef and any accumulated juices to the skillet. Stir and cook until the beef is fully cooked and the sauce coats the beef and vegetables, about 2–3 minutes more.
Transfer the beef and broccoli to plates over cauliflower rice or white rice if desired. Sprinkle with 1 tablespoon toasted sesame seeds and the sliced scallions before serving.