Prepare the beef by patting the flank steak dry with paper towels, then slicing it thinly against the grain into bite-sized strips and seasoning the slices with the fine sea salt and freshly ground black pepper.
In a small bowl, whisk together the low-sodium soy sauce or tamari, oyster sauce, toasted sesame oil, water, cornstarch, brown sugar, and crushed red pepper flakes if using, until the cornstarch and sugar are fully dissolved and the sauce looks smooth and glossy.
Place the broccoli florets in a colander and rinse under cool water, then shake off any excess moisture; if using frozen broccoli, make sure it is fully thawed and patted dry so it stir-fries instead of steaming.
Heat 1 tablespoon of the neutral oil in a large skillet or wok over medium-high heat until it shimmers, then add the sliced beef in a single layer, cooking for 2 to 3 minutes without stirring to develop some browning before tossing and stir-frying for another 1 to 2 minutes until the strips are mostly cooked through but still tender; transfer the beef and any juices to a plate and set aside.
Add the remaining 1 tablespoon of neutral oil to the same skillet or wok over medium-high heat, then add the broccoli florets and stir-fry for 3 to 4 minutes, tossing frequently, until the broccoli is bright green and crisp-tender.
Reduce the heat to medium, push the broccoli to the edges of the pan to create a space in the center, then add the minced garlic and grated ginger to the center and cook, stirring constantly, for about 30 seconds until fragrant but not browned.
Give the prepared sauce a quick stir to redistribute the cornstarch, then pour it into the pan, stirring it into the garlic, ginger, and broccoli; cook for 1 to 2 minutes, stirring often, until the sauce begins to thicken and lightly coat the broccoli.
Return the cooked beef and any accumulated juices to the pan, tossing everything together so the beef and broccoli are evenly coated in the glossy sauce, and cook for another 1 to 2 minutes until the beef is heated through and the sauce has thickened to your liking; taste and adjust the seasoning with a pinch more fine sea salt or black pepper if needed before serving hot.