Heat 1 teaspoon of vegetable oil in a large skillet over medium heat. Add the broccoli florets and cook for about 4 minutes, or until they are just tender. Stir in the minced ginger and garlic, cooking for an additional 30 seconds until fragrant. Transfer the broccoli mixture to a plate and cover to keep warm. Wipe the skillet clean with a paper towel, then increase the heat to high and add the remaining tablespoon of oil. Season the sliced flank steak with salt and pepper, and place the pieces in the skillet in a single layer—work in batches if necessary. Sear the beef for 3 to 4 minutes on each side until it is browned and cooked through. Return the broccoli mixture to the skillet and stir to combine, cooking for another 2 minutes until everything is heated through.

In a mixing bowl, whisk together the oyster sauce, beef broth (or water), sugar, sesame oil, and soy sauce. In a separate small bowl, combine the cornstarch with 1 tablespoon of cold water and stir to dissolve. Pour the sauce mixture over the beef and broccoli in the skillet and cook for 30 seconds. Stir in the cornstarch slurry and bring everything to a boil. Let it cook for 1 additional minute, or until the sauce begins to thicken slightly. Serve hot, optionally over steamed rice.