Cook the noodles. Bring a large pot of salted water to a boil. Cook egg noodles according to package instructions until just tender. Drain and set aside. Toss with a little olive oil to prevent sticking.

Brown the beef. In a large skillet over medium-high heat, add the olive oil. Add the ground beef, season with salt and pepper, and cook, breaking it up with a spatula, until nicely browned and no pink remains, about 5–7 minutes. Transfer the beef to a plate and drain excess grease if needed, leaving about 1 tablespoon in the pan.

Sauté the vegetables. Reduce heat to medium. Add 1 tablespoon butter, then the onions. Cook until softened and lightly golden, 3–4 minutes. Add mushrooms and a pinch of salt. Cook, stirring occasionally, until the mushrooms release their liquid and brown, about 6–8 minutes. Add garlic and cook 30 seconds until fragrant.

Make the roux. Push the mushrooms and onions to the sides of the skillet. Melt the remaining 1 tablespoon butter in the center, then sprinkle in the flour. Stir the flour into the butter for 1 minute to cook off the raw taste.

Build the sauce. Slowly whisk in the beef broth, scraping up any browned bits from the bottom of the pan. Stir in Worcestershire, Dijon, and paprika if using. Bring to a gentle simmer and cook 3–4 minutes, until slightly thickened.

Combine the beef and sauce. Return the browned ground beef and any juices to the skillet. Stir to coat and simmer 2–3 minutes to marry the flavors. Taste and adjust salt and pepper.

Finish with sour cream. Turn the heat to low. Off the heat, stir in the sour cream until the sauce is smooth and creamy. If the sauce seems too thick, add a splash of warm water or broth to loosen.

Toss with noodles and serve. Add the cooked noodles to the skillet and toss gently to coat. Sprinkle with fresh parsley and serve hot.