Heat the oil and butter in a large skillet over medium-high heat. Season the beef strips with salt and pepper. Sear the beef in the skillet until browned on both sides, about 2-3 minutes per side. Remove the beef and set aside.
In the same skillet, add the chopped onion and the mushrooms and cook until softened, about 3-4 minutes.
In a small bowl, mix the flour with a little bit of sour cream to create a smooth paste. Add this mixture to the skillet and stir well.
Gradually add the remaining sour cream and mustard, stirring constantly to avoid lumps. Add the meat broth and season with salt and pepper to taste. Let the sauce simmer for a few minutes until slightly thickened.
Return the seared beef to the skillet, mixing it well with the sauce. Cook for an additional 2-3 minutes until the beef is heated through.
Serve the beef stroganoff over cooked egg noodles or rice. Garnish with freshly chopped dill or parsley if desired.
