Place the noodles in a large pot and cover them with room-temperature tap water. Allow them to rest for 1 to 2 hours. They will become soft but still have a little resistance.
Slice the steak into ¼-inch strips. Place in a medium-sized bowl.
In a small bowl, whisk together the soy sauce, 1 tablespoon of the rice wine, the cornstarch, 1 teaspoon of the sesame oil, and brown sugar, until starch and sugar are dissolved.
Pour over the steak and turn to coat. Let stand for 20 minutes to 2 hours.
Drain the noodles and toss with the remaining 1 teaspoon sesame oil.
Next, make a sauce by whisking together the oyster sauce, black bean sauce, 1 tablespoon of water, and the remaining 1 tablespoon of rice wine in a small bowl. Set aside.
Heat 1 tbsp of the oil in a large wok (or skillet) over high heat.
Add the steak and the marinade. Cook until starting to brown, about 2 - 3 minutes. Add the garlic and ginger, and stir-fry until the steak is just no longer pink, about another 1 -2 minutes more. Transfer the mixture to a platter.
Return the wok to high heat. Add the remaining 2 tablespoons the oil to the wok. Add the onion and cook, without stirring, until browned on the edges, about 2 minutes. Add the broccoli and scallions and stir-fry until the broccoli is crisp-tender, about 2 minutes.
Add the rice noodles and steak mixture and stir-fry until the noodles are hot, about another 1 - 2 minutes.
Add the sauce mixture and stir until the noodles are coated.
Garnish with extra scallion slices and toasted sesame seeds. Serve at once.
