Bring a large pot of salted water to a boil. Add the dried egg noodles or thin wheat noodles and cook according to the package directions until just tender. Drain well and set aside.

While the noodles cook, slice the flank steak thinly against the grain into bite-sized strips and pat the pieces dry with paper towels.

In a small bowl, whisk together the low-sodium soy sauce, oyster sauce, hoisin sauce, brown sugar, cornstarch, water, black pepper, red pepper flakes if using, and salt until the cornstarch is fully dissolved and the mixture is smooth. Set this stir fry sauce aside.

Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the broccoli florets and stir fry for 3 to 4 minutes until they turn bright green and are just starting to become tender but still crisp. Transfer the broccoli to a plate and set aside.

In the same skillet or wok, add the remaining 1 tablespoon of vegetable oil. Add the sliced flank steak in a single layer and cook for 2 to 3 minutes, stirring occasionally, until the beef is browned on the outside and mostly cooked through.

Push the beef to one side of the skillet. Add the minced garlic and grated ginger to the empty side and cook for about 30 seconds, stirring constantly, until fragrant but not browned.

Pour the prepared stir fry sauce into the skillet. Stir everything together, scraping up any browned bits from the bottom, and let the sauce come to a gentle simmer for 1 to 2 minutes until it begins to thicken and coat the beef.

Return the cooked broccoli florets to the skillet. Toss them with the beef and sauce until everything is evenly coated and the broccoli is heated through.

Add the drained cooked noodles to the skillet along with the sesame oil. Use tongs to gently toss the noodles with the beef, broccoli, and sauce until the noodles are fully coated and everything is well combined.

Taste and adjust seasoning with a pinch more salt if needed. Remove the skillet from the heat, sprinkle the sliced green onions over the top, and serve the beef and broccoli stir fry with noodles hot.