In a large skillet heat oil over medium-high heat until very hot. Add steak. Do not add any liquid and do not cover the skillet. Reduce heat to medium and cook for 10 to 13 minutes or to desired doneness, turning meat occasionally. If meat browns too quickly, reduce heat to medium-low. Transfer meat to platter; keep warm.
Add garlic and red pepper to skillet; cook for 10 seconds. Remove skillet from heat. Carefully add wine. Return to heat. Boil, uncovered, about 5 minutes or until most of the liquid is evaporated. Add mushrooms, vinegar, soy sauce, and honey; return to simmer. Cook and stir about 4 minutes or until mushrooms are tender. Stir in butter until melted. Spoon over steak.