Slice steak thinly on the bias (this will be easier if you freeze the steak for 20-30 minutes first). Combine in a bowl with soy sauce, Worcestershire sauce and hot sauce. Let stand 10-15 minute.
Heat oil in heavy skillet. Add beef and stir-fry quickly until meat loses its pink color. Remove from pan to a clean plate and set aside.
Add onion, green pepper and garlic to fat remaining in skillet. Sauté until soft. Add mushrooms with their liquid.
Stir cornstarch into a little bit of the beef broth until smooth. Add the slurry with the rest of the broth to the vegetables. Bring to a boil and cook 3 minutes. Return meat to pan and cook until hot all the way through.