Bring a large pot of salted water to a boil. Add the egg noodles and cook according to the package directions until al dente, about 7–9 minutes. Drain well and toss with a small amount of butter or oil to keep the noodles from sticking. Set aside.
While the noodles cook, melt 1 tablespoon of butter in a large skillet over medium-high heat. Add the ground beef, breaking it into crumbles as it cooks. Brown the beef until no longer pink, about 6–8 minutes. Season lightly with salt and black pepper, then transfer the beef to a plate. Leave any drippings in the skillet for extra flavor.
Add the remaining tablespoon of butter to the same skillet. Stir in the chopped onion and cook until softened, about 3–4 minutes. Add the sliced mushrooms and continue cooking for 5–7 minutes, or until they release their moisture and begin to brown. Stir in the minced garlic and cook for another 30 seconds, just until fragrant.
Sprinkle the flour over the mushroom mixture, stirring constantly for 1–2 minutes to remove the raw flour taste. Slowly whisk in the beef broth, stirring continuously until smooth. Add the Worcestershire sauce and smoked paprika, then bring the mixture to a gentle simmer. Cook for 3–5 minutes, or until the sauce has thickened.
Return the cooked ground beef to the skillet and stir until it's evenly coated in the creamy sauce. Reduce the heat to low.
Remove the skillet from the heat and gently stir in the sour cream until the sauce is smooth and creamy. Taste and season with additional salt and pepper if needed.
Add the cooked egg noodles to the skillet and gently toss until everything is well coated in the sauce. Garnish with freshly chopped parsley, if desired, and serve immediately while hot.