In a medium bowl, combine the flour, salt, and black pepper. Toss the beef strips in the flour mixture until evenly coated.
Heat 1 tablespoon of butter and the olive oil in a large skillet over medium-high heat. Add the beef strips in a single layer and cook for 2-3 minutes per side until browned but not fully cooked through. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of butter. Add the chopped onion and cook for 3-4 minutes until softened.
Add the minced garlic and sliced mushrooms to the skillet. Cook for 5-6 minutes until the mushrooms are browned and tender.
Pour in the beef broth and stir in the Dijon mustard. Bring the mixture to a simmer and cook for 5 minutes to reduce slightly.
Reduce the heat to low and stir in the sour cream until the sauce is smooth. Return the beef strips to the skillet and cook for an additional 3-4 minutes until the beef is cooked through and heated.
Meanwhile, cook the egg noodles according to package instructions. Drain and set aside.
Serve the beef stroganoff over the cooked egg noodles and garnish with chopped fresh parsley.