Set the oil on medium heat. Add the onions, bell pepper, celery and garlic, and sauté for about 5 minutes.
Stir in the flour evenly with the vegetables. Heat for another 3 minutes, stirring continuously.
Pour in the beef broth and continue stirring. When the mixture is smooth, add the steak strips and Cajun Seasoning. Cover, then reduce heat to a low simmer and let it cook for 1 hour.
Add the wine, Tabasco and Worcestershire, and stir. Cover again and let the mixture cook for forty more minutes.