Preheat oven to 450°F and line a large sheet pan with parchment paper.
Whisk together the soy sauce, sesame oil, honey, garlic, ginger, and red pepper flakes, then transfer half the sauce to a separate clean bowl and reserve it for the beef.
Add the broccoli, bell peppers, and onion to the sauce remaining in the first bowl and toss to coat. Spread them in a single layer on the prepared pan and roast for 10 minutes.
Toss the sliced beef with the remaining sauce. Remove the pan from the oven, move the vegetables aside, and arrange the beef in a single layer.
Roast for 6 to 10 minutes more, stirring once, until the vegetables are tender and slightly charred and the beef is cooked to the desired doneness.
Serve immediately over rice or noodles, drizzled with any pan juices.