Bring a large pot of salted water to a boil and cook the egg noodles according to package directions. Drain well, then return them to the pot and stir in 2 tablespoons butter until coated. Cover to keep warm.
Heat 1 tablespoon butter in a large skillet over medium-high heat. Add the beef strips, season with salt and pepper, and cook until browned on all sides. Remove the beef to a plate and set aside.
In the same skillet, add the onion and mushrooms. Cook until the onion softens and the mushrooms release their liquid.
Stir in the garlic and cook for 30 seconds until fragrant. Sprinkle the flour over the vegetables and stir for 1 minute.
Slowly pour in the beef broth and Worcestershire sauce while stirring. Bring the mixture to a gentle simmer until it thickens slightly.
Reduce the heat to low and stir in the sour cream until smooth. Return the beef to the skillet and heat everything through for 2 minutes. Taste and adjust salt and pepper if needed.
Divide the buttered noodles among four plates and spoon the beef and sauce over the top. Finish with chopped parsley.