Cook the noodles: Bring a large pot of salted water to a boil. Cook egg noodles according to package directions until just tender.
Drain and set aside. Toss with a little olive oil if they’ll sit for a while.
Brown the beef: In a large skillet over medium-high heat, add ground beef (and oil if your beef is very lean). Cook, breaking it up, until browned with some crispy bits, about 5–7 minutes.
Season with a pinch of salt and pepper. Spoon off excess fat if needed, leaving about 1 tablespoon in the pan.
Soften the aromatics: Add the chopped onion and sliced mushrooms to the skillet. Cook, stirring occasionally, until the onions are soft and the mushrooms release their moisture and start to brown, 5–6 minutes.
Add the garlic and cook 30 seconds, just until fragrant.
Make the roux: Sprinkle the flour over the beef and vegetables. Stir well to coat and cook for 1 minute to eliminate the raw flour taste.
Build the sauce: Stir in Worcestershire sauce, Dijon mustard, and paprika. Slowly pour in the beef broth while stirring, scraping up any browned bits from the bottom of the pan.
Bring to a gentle simmer and cook 3–4 minutes, until slightly thickened.
Finish creamy: Reduce heat to low. Stir in the sour cream until smooth. If the sauce seems too thick, add milk or half-and-half a splash at a time until it’s silky and coats a spoon.
Taste and adjust with salt and pepper.
Combine: Add the cooked egg noodles to the skillet and toss gently to coat in the sauce. Warm through for 1–2 minutes so the noodles absorb some flavor.
Serve: Sprinkle with chopped parsley and a few cracks of black pepper. Serve hot with a simple green salad or steamed vegetables.