Mix together two tablespoons of soy sauce with 1 teaspoon of sugar in a medium bowl. Add beef and marinate for one hour.
Mix two tablespoons of soy sauce and two tablespoons of sugar, chicken broth, pepper flakes, and cornstarch in a medium bowl and set aside. Mince garlic, ginger and one teaspoons of vegetable oil in a small bowl and set aside.
Add one Tablespoon of oil to the pan and cook one half of the beef mixture. Cook for about one minute without stirring the beef, then stir and cook until browned. Remove beef to a medium bowl cook remaining beef in the same manner.
Add one tablespoon of oil to a 12 inch non-stick skillet and heat oil until light wisps of smoke appear. Add mushrooms and cook until they begin to brown, about two minutes. Add green beans and carrots and cook until spotty brown. Add water to skillet and cover with lid. Continue to cook about 2 minutes. Remove lid.
Push vegetables to the sides of the skillet and add garlic-ginger mixture to the center of the pan. Cook 15 to 20 seconds until fragrant and mix vegetables back into garlic-ginger.
Add cooked beef to the vegetable mixture and stir to combine. Whisk soy sauce / chicken broth mixture and add to skillet. Add green onions and stir to combine.
Serve over rice.