Prepare the beef by patting the flank steak dry with paper towels, then slicing it thinly against the grain into bite-sized strips so it cooks quickly and stays tender.

Place the sliced beef in a bowl and season it lightly with the ground black pepper and a small pinch of the salt, tossing to coat the pieces evenly.

In a separate small bowl, whisk together the soy sauce, beef broth, oyster sauce, brown sugar, rice vinegar, crushed red pepper flakes if using, and sesame oil until the sugar dissolves and the liquids are well combined; set this garlic sauce base aside.

In another small bowl, stir the cornstarch together with the water until completely smooth, forming a slurry with no visible lumps; keep this nearby to thicken the sauce later.

Bring a medium pot of water to a gentle boil and add the broccoli florets, cooking them for 1 to 2 minutes just until they turn bright green and slightly tender, then immediately drain them well.

Rinse the drained broccoli briefly under cold running water or place it in a bowl of cold water to stop the cooking, then drain again thoroughly and set aside so it stays crisp-tender.

Heat 2 tablespoons of the vegetable oil in a large skillet or wok over medium-high heat until the oil is hot and shimmering but not smoking.

Add the seasoned beef to the hot pan in an even layer, cooking it for about 3 to 4 minutes, stirring occasionally, until the strips are browned on the outside and just cooked through; transfer the cooked beef to a clean plate and keep it nearby.

Return the skillet or wok to the heat and add the remaining 1 tablespoon of vegetable oil, allowing it to warm for a few seconds.

Add the minced garlic and grated ginger to the pan, stirring constantly for about 30 seconds to 1 minute until fragrant, being careful not to let the garlic brown too deeply.

Give the prepared garlic sauce base a quick stir, then pour it into the skillet with the garlic and ginger, bringing the mixture to a gentle simmer over medium heat.

Stir the cornstarch slurry once more, then slowly pour it into the simmering sauce while stirring continuously, allowing the sauce to thicken to a glossy, smooth consistency over 1 to 2 minutes.

Reduce the heat to medium-low, then return the cooked beef and the blanched broccoli florets to the pan, tossing everything together so the meat and vegetables are evenly coated in the thickened garlic sauce.

Let the beef and broccoli simmer gently in the sauce for another 2 to 3 minutes so the flavors meld and the broccoli is heated through, then taste and adjust the seasoning with the remaining salt if needed before serving hot.