Soak the shiitake mushrooms in a bowl of warm water till pliable and soft, 20 minutes. Remove them straining the soaking water through a sieve or cheese cloth and reserve water. Slice up the mushrooms and set aside.
Meanwhile, slice up the chicken into thin pieces and coat with 1 tbsp. soy sauce, sesame oil, and 2 tbsp. cornstarch. Allow the chicken to marinate for 20 minutes.
In a heated wok or large sauté pan, add the safflower oil and briefly fry the chicken strips.
Add the ginger and garlic and toss together coating evenly. Add the broccoli and 1/2 of the shiitake water to the pan and cover steaming for 5 minutes until the broccoli is cooked. Add the scallions and remaining soy sauce to the pan and cook 1 minute longer.