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Season the steak salt, pepper, and 1 tablespoon flour. Heat the oil in a large (12 inch) skillet over medium-high heat. Add the steak strips and let them cook undisturbed for 4-5 minutes so a brown crust forms. Add the mushrooms, onions, and garlic and sauté until the onions are soft, about 4 minutes. Transfer the mixture to a large bowl or plate and set aside.
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Reduce the heat to medium and melt butter using the same pan. Whisk in the remaining 3 tablespoons of flour and cook the roux for 1-2 minutes. Slowly pour in the beef broth a little at a time while whisking continuously until smooth and thickened. Add the red wine vinegar, Worcestershire sauce, and thyme. Scoop out 1/3 cup of the sauce and reserve to pour over the steak at the end.
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Bring the mixture to a boil and then pour in the noodles. Stir to coat and reduce the heat to medium-low. Cook for about 10-14 minutes, stirring occasionally, and if needed add in an extra 1/3 cup broth or more as needed.
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Once the noodles are al dente, add the cream cheese and sour cream and stir until smooth and combined. Season additionally with salt, black pepper, and Worcestershire sauce as needed.
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Add the steak and onions back in the pan and drizzle reserved sauce over the steak. Cook until heated through, about 1-2 minutes. Serve hot in individual bowls and garnish with parsley and, freshly black pepper if desired.