In a medium bowl, combine the soy sauce, oyster sauce, cornstarch, beef broth, sesame oil, and sugar. Whisk until smooth and set aside.
Heat the 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 broccoli florets and stir-fry for 2-3 minutes until they are bright green and slightly tender. Add the minced garlic and ginger, and stir-fry for an additional 30 seconds.
Return the beef to the skillet and pour the sauce mixture over the beef and broccoli. Stir well to combine and cook for another 2-3 minutes until the sauce thickens and everything is heated through.
Remove from heat and garnish with sliced green onions. Serve over cooked rice.