For ultra-thin slices, pop the steak in the freezer for 15–20 minutes. Slice across the grain into 1/4-inch strips. Toss the beef with 1 teaspoon Worcestershire, 1 teaspoon whole-grain Dijon, and the smoked paprika; set aside at room temperature while you start the sauce.
Bring a large pot of salted water to a boil and cook the egg noodles until just tender. Drain and toss with a drizzle of oil to prevent sticking; keep warm.
Set a wide skillet over medium-high heat and melt the butter. Add the mushrooms in an even layer and cook without stirring for 3 minutes. Add the onion, season lightly with salt and pepper, and continue cooking, stirring occasionally, until well browned and tender, 6–8 minutes more. Stir in the thyme and garlic and cook 30 seconds until fragrant.
Sprinkle the flour over the vegetables and cook, stirring, for 1 minute. Gradually whisk in the beef broth until smooth. Stir in the remaining 1/2 teaspoon Worcestershire and the remaining 1 teaspoon mustard. Reduce heat to medium and let the sauce simmer gently for 5–6 minutes to thicken slightly.
Scoop about 1/2 cup of the hot sauce into a bowl and whisk it into the sour cream to temper it. Set aside off the heat.
Heat the neutral oil in a second skillet over high heat. Pat the marinated beef dry, season lightly with salt and pepper, and sear in two quick batches, 30–45 seconds per side, just until browned but still pink inside. Transfer to a plate and rest 2 minutes.
Lower the mushroom sauce to the gentlest simmer. Stir in the tempered sour cream until the sauce turns silky; do not let it boil. Add any resting juices from the beef, then fold in the seared steak. Warm through for 1–2 minutes and adjust seasoning with salt and pepper.
Serve the beef and sauce over the warm egg noodles and finish with chopped parsley.