Prepare the Beef: In a bowl, toss the beef slices with flour, paprika, salt, and black pepper until evenly coated.
Sear the Beef: Heat a large skillet over medium-high heat. Add the olive oil and sear the beef in batches until browned on all sides. Remove from the skillet and set aside.
Sauté the Vegetables: Reduce the heat to medium and add butter to the skillet. Sauté the onions and garlic until softened, about 2–3 minutes. Add the mushrooms and cook until tender and golden, about 5 minutes.
Build the Sauce: Pour in the beef broth and bring to a simmer, scraping up any browned bits from the skillet. Stir in the sour cream, Dijon mustard, Worcestershire sauce, and smoked paprika (if using). Mix well and cook until the sauce is smooth and slightly thickened, about 3–5 minutes.
Combine and Serve: Return the seared beef to the skillet and simmer for 2–3 minutes, just until heated through. Serve the stroganoff over cooked egg noodles, garnished with fresh parsley.