Combine soy sauce, Worcestershire sauce, minced garlic and steak in a sealed bag. Marinade in refrigerator overnight.
Heat a cast iron skillet with 1 tablespoon of olive oil over medium heat. Add steaks to skillet and cook on each side for about 8 minutes or until steaks reach desired temperature (145°F medium rare, 160°F medium, 170°F well done).
Remove steaks from skillet and add remaining 2 tablespoons olive oil, mushrooms and onions over medium heat. Cook until vegetables are tender.
Add red wine and cook until no liquid remains.
Top steaks with mushrooms and onions.