Prep the beef. Freeze the steak for 20 minutes to firm it up.
Slice thinly against the grain. Toss with 2 tablespoons cornstarch, 1/2 teaspoon black pepper, and a pinch of salt. Set aside while you prep the sauce and vegetables.
Whisk the sauce. In a bowl, combine soy sauce, dark soy (if using), brown sugar, garlic, ginger, rice vinegar, sesame oil, and broth.
Whisk in 1 tablespoon cornstarch until smooth. Adjust heat with red pepper flakes or sambal.
Cook the noodles. Boil according to package directions until just shy of al dente. Drain and rinse briefly under cool water to stop the cooking.
Toss with a teaspoon of oil to prevent sticking and set aside.
Sear the beef. Heat a large skillet or wok over medium-high until hot. Add 1–2 tablespoons oil. Spread the beef in a single layer and sear undisturbed for 1–2 minutes, then stir-fry another 1–2 minutes until browned but not overcooked.
Work in batches if needed. Transfer to a plate.
Stir-fry the vegetables. Add a splash more oil if the pan is dry. Stir-fry broccoli for 2 minutes, then add bell pepper and carrot.
Cook until crisp-tender, about 2–3 more minutes. Add the white/light green parts of the green onions and cook 30 seconds.
Make it sticky. Pour in the sauce and bring to a simmer. It will start to thicken and turn glossy in about 1–2 minutes.
If it gets too thick, add a splash of water or broth.
Toss it all together. Return the beef to the pan with any juices. Add the noodles and the dark green parts of the green onions. Toss with tongs until everything is coated and heated through, about 1 minute.
Taste and finish. Adjust salt, soy, or heat as needed.
Sprinkle with sesame seeds. Serve hot.