Melt the butter in a large skillet over medium high heat. Add the mushrooms and sauté until light golden brown. Remove the mushrooms from the pan and set aside.
Add the onions to the skillet and cook for 3-5 minutes until they start to soften. Reduce heat to low and add garlic and return the mushrooms to the pan; sauté for 30-60 seconds until the garlic is fragrant. Remove the mixture from the skillet and set aside.
In a large bow, toss together the slices of steak, 2 tablespoons of the flour, salt, and pepper and stir to coat.
Add the olive oil to the skillet over medium high heat. Add steak and cook just until browned, then remove from the skillet and set aside.
Reduce the heat to low and add the red wine to skillet and deglaze the pan by scraping up the brown bits from the bottom. Pour 1/2 cup of beef broth in bowl and set aside. Add the remaining beef broth and the worcestershire sauce to the skillet. Simmer for 5 minutes, stirring occasionally.
In small bowl whisk together the reserved ½ cup of beef broth and the 1/4 cup flour. Whisk this flour mixture into the skillet with the wine and beef broth mixture. Cook for 2 minutes until slightly thickened.
Add the steak and mushroom mixture back to the skillet and simmer for 5-10 minutes.
Serve the steak bites over egg noodles or mashed potatoes.