Prepare egg noodles according to package directions; drain, butter, and keep warm.
Meanwhile, take beef out of freezer and cut steak lengthwise in half.
Then, with knife held in slanting position almost parallel to the cutting surface, slice each half across width into 1/8-inch thick slices.
Thickly slice the mushrooms and coarsely chop onion.
In a 12-inch nonstick skillet over high heat, cook the meat, stirring quickly and constantly, until browned, about 2 minutes; remove to plate or bowl (it may be necessary to brown the beef in two batches).
In same skillet over medium-high heat, in hot oil, cook mushrooms and onion until tender.
In a cup, mix flour with ½ cup water; stir into mushroom mixture with beef broth, Worcestershire, salt and sugar.
Over high heat, heat to boiling.
Reduce heat to medium and cook until mixture thickens slightly.