Mix the soy sauce, oyster sauce, and cornstarch in a small bowl until smooth. Set the sauce aside.
Heat 1 tablespoon of vegetable oil in a large skillet over medium-high heat. Add the sliced flank steak and cook for 2 to 3 minutes until browned. Remove the beef from the skillet and set it aside.
Add the remaining tablespoon of oil to the same skillet. Stir in the minced garlic and broccoli florets. Cook for 3 to 4 minutes, stirring often, until the broccoli turns bright green.
Return the cooked beef to the skillet. Pour the prepared sauce over the mixture and stir well. Cook for another 2 minutes until the sauce thickens and coats everything evenly.
Spoon the stir-fry over the cooked steamed rice and serve right away.