Pop the flank steak in the freezer for 15 minutes to firm it up, then slice it against the grain into thin strips about ¼ inch (6 mm) wide.
Toss the sliced beef with 3 tablespoons soy sauce, the Shaoxing wine, and 1 tablespoon cornstarch until every strip is coated. Let it sit for at least 15 minutes.
Whisk together the beef broth, remaining 2 tablespoons soy sauce, oyster sauce, sesame oil, sugar, and black pepper in a bowl. Stir the 1 tablespoon cornstarch into 2 tablespoons water in a separate cup until smooth.
Slice the bell peppers and onion, and mince the garlic and ginger so everything is ready to go.
Heat 2 tablespoons vegetable oil in a wok or large skillet over high heat until it shimmers. Add the beef in a single layer, working in two batches, and sear undisturbed for about 1 minute, then stir for another minute until browned but not fully cooked through. Transfer to a plate.
Add the last 1 tablespoon oil to the same pan over medium-high heat. Stir-fry the onion and bell peppers for 2 to 3 minutes until tender-crisp, then add the garlic and ginger and stir for about 30 seconds until fragrant.
Return the seared beef and any resting juices to the pan. Pour in the sauce mixture and bring to a gentle simmer. Stir the slurry, pour it in, and cook for 1 to 2 minutes, stirring, until the sauce turns glossy and thick enough to coat the beef.
Taste and add more black pepper if desired. Scatter sliced green onions over the top and serve right away over hot rice or noodles.