DO-AHEAD TIP: Steam broccoli.
Heat 1 1/2 teaspoons of oil in a skillet or wok over medium-high heat; add beef strips and stir-fry for 5 minutes or till browned and cooked to the desired level of doneness.
Add white pepper and salt then remove from skillet and keep warm.
Heat remaining oil in the skillet or wok; add garlic, gingerroot, and mushrooms; stir-fry for 2 minutes. Add beef strips and steamed broccoli florets.
In a small bowl, whisk together cornstarch, soy sauce and broth to a smooth paste; add to skillet or wok and cook for 30 seconds or until thickened; add the sesame oil, blend well and serve.