Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced flank steak and stir-fry for about 3-4 minutes until browned. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the sliced onion, red bell pepper, and broccoli florets. Stir-fry for about 4-5 minutes until the vegetables are tender-crisp.
Add the minced garlic and grated ginger to the skillet, cooking for an additional 1 minute until fragrant. Return the beef to the skillet.
In a small bowl, mix together the soy sauce, brown sugar, and rice vinegar. Pour this mixture over the beef and vegetables, stirring to combine. Cook for another 2 minutes.
Stir in the cornstarch mixture to thicken the sauce, cooking for an additional minute until the sauce is glossy and coats the beef and vegetables.
Serve the ginger beef stir-fry over cooked rice and garnish with sliced green onions.