Bring a large pot of salted water to a boil over high heat. Add the wide egg noodles and cook according to the package directions until just al dente, usually about 7–9 minutes. Stir occasionally to keep them from sticking.

Once the egg noodles are al dente, drain them well in a colander and set aside. If you like, toss them with a small splash of olive oil to prevent sticking while you prepare the sauce.

While the noodles cook, place a large deep skillet or wide saucepan over medium heat. Add the unsalted butter and olive oil, allowing the butter to melt completely and become slightly foamy without browning.

Add the finely chopped yellow onion to the skillet. Sauté, stirring frequently, for about 5–7 minutes, or until the onion turns soft and translucent with lightly golden edges.

Stir in the minced garlic and cook for 30–60 seconds, just until fragrant. Avoid letting the garlic brown, as it can become bitter.

Sprinkle the all-purpose flour evenly over the onion and garlic mixture. Stir constantly for about 1–2 minutes to coat the vegetables and cook off the raw flour taste, forming a thick paste-like roux.

Slowly pour in the beef broth while whisking or stirring continuously to avoid lumps. Continue stirring until the flour is fully incorporated and the mixture is smooth.

Add the Worcestershire sauce, dried thyme, dried parsley, salt, and black pepper to the skillet. Stir well, then bring the sauce to a gentle simmer. Let it cook for 5–7 minutes, stirring occasionally, until slightly thickened and glossy.

Add the shredded leftover roast beef to the simmering sauce. Stir to coat the beef evenly, then let it warm through for about 3–4 minutes, allowing the flavors to mingle and the meat to become tender in the gravy.

Reduce the heat to low. Stir in the sour cream until fully blended, creating a creamy, velvety sauce. Avoid boiling the sauce at this stage to prevent the sour cream from curdling.

Add the grated Parmesan cheese and stir until it melts smoothly into the sauce, enriching the texture and flavor. Taste the sauce and adjust seasoning with additional salt or black pepper if needed.

Gently add the cooked egg noodles to the skillet with the creamy beef sauce. Toss carefully with tongs or a large spoon until all the noodles are thoroughly coated and the beef is evenly distributed throughout the dish.

Allow the beef and noodles to sit over low heat for 1–2 minutes, just until everything is piping hot and the sauce clings nicely to the pasta. If the mixture seems too thick, you can loosen it with a splash of extra beef broth.

Remove the skillet from the heat. Sprinkle the chopped fresh parsley over the top for a bright, fresh finish. Serve the beef and noodles hot, spooning generous portions into bowls or onto plates.