Thinly slice beef and pat dry.
Stir 2 tbsp soy, 1 tbsp cornstarch, half the ginger, half the garlic, sesame oil, and pepper.
Toss beef with the mixture; marinate 10 minutes while prepping vegetables.
Whisk remaining soy, brown sugar, rice vinegar, broth, remaining cornstarch, and red pepper flakes.
Heat a wok over high heat; add 1 tbsp neutral oil.
Sear beef in two quick batches until browned, 1–2 minutes total. Transfer to a plate.
Add remaining oil; stir-fry broccoli 2 minutes.
Add bell pepper; cook 1 minute until crisp-tender.
Return beef and any juices; pour in the sauce.
Stir until glossy and thick, 1–2 minutes. Taste and salt if needed.
Finish with green onions and sesame seeds. Serve over rice or noodles.