Place a large pan over high heat and add the vegetable oil. Wait until the oil shimmers and gives off the faintest wisp of smoke.
Arrange the flank steak in one uncrowded layer and season it with salt and pepper. The strips should make an immediate, active sizzle when they touch the pan.
Leave the steak to brown for 3-4 minutes per side, working in batches as needed. Look for browned edges and avoid letting the pan fill with pale liquid.
Transfer the browned steak to a plate and cover it to hold in warmth. The beef will stay juicy while the vegetables cook.
Cook the broccoli, celery, and bell pepper for 4-5 minutes, seasoning with salt and pepper, then stir in the baby corn and garlic for 30 seconds. The broccoli should stay bright green, and the garlic should smell fragrant rather than dark or bitter.
Return the beef and any collected juices to the pan with the vegetables. Keep everything moving so the steak warms through without overcooking.
Whisk the beef broth, soy sauce, oyster sauce, rice vinegar, honey, chili paste, and cornstarch in a small bowl. The mixture should look smooth, with no cornstarch settled at the bottom.
Pour the sauce into the pan, bring it to a simmer, and cook for 1-2 minutes. It is ready when it bubbles into a glossy glaze that coats the beef and vegetables.