Boil the noodles until just al dente; drain, rinse with cold water, and set aside. Heat a large skillet or wok over high heat, add 1 tbsp vegetable oil, and sear the beef in a single layer for 2-3 minutes until browned but still pink inside. Transfer to a plate.

Add a splash of oil if the pan is dry, then add the broccoli and 2 tbsp water. Cover and steam for 2 minutes. Uncover, add the garlic and ginger, and stir-fry 1 minute until fragrant.

Add the drained noodles and the sauce mixture (soy sauce, oyster sauce, brown sugar, cornstarch, broth, and sesame oil whisked together). Toss for about 2 minutes until the sauce thickens and coats everything.

Return the beef and any juices to the pan, toss for 30 seconds to combine, then turn out onto a platter and scatter with green onions and sesame seeds. Serve immediately.