Place the flour and sliced beef in a zip-lock bag, seasoning with salt and pepper. Shake the bag until the beef is evenly coated.
In a large skillet, heat 1 1/2 tablespoons of butter with 2 teaspoons of olive oil over high heat until the mixture bubbles. Add half of the beef and cook, stirring occasionally, for 3-5 minutes until browned. Transfer the beef to a plate and repeat the process with the remaining butter, oil, and beef.
Lower the heat to medium and add the remaining olive oil to the pan. Add the sliced onion and mushrooms, cooking and stirring for about 5 minutes until they soften. Stir in the minced garlic and sweet paprika, cooking for an additional minute.
Pour in the beef broth, tomato paste, and Dijon mustard. Add the browned beef back into the pan, stirring everything together. Bring the mixture to a boil, then reduce the heat to low and simmer for 5 minutes, allowing the sauce to thicken slightly.
Finally, stir in the crème fraîche until well combined. Serve the beef stroganoff over cooked fettuccine, garnished with fresh parsley.