Cut brocolli into 1 1/2 inch strips, about 1/2 inch thick. Set aside. Cut Steak into 2 inch slices. In a small bowl, combin 1 teaspoon cornstarch, 1/4 teaspoon salt, ginger, soy sauce, 1 1/2 teaspoons water, and garlic. Blend well. Mix beef with marinade, set aside.
Preheat wok or large skillet. Add 2 tablespoons oil and heat 30 seconds. Add beef and brown until just slightly pink. Return beef to bowl. Add remaining 3 tablespoons oil to skillet or wok. Add brocolli, bamboo shoots and mushrooms. Stir fry until brocolli is tender ( about 5 minutes) Add salt, remaining sugar, 3 tablespoons water, and remaining cornstarch. Bring to boil. Return meat and heat 1 minute.
