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 sauté for 3-4 minutes until softened.
Add the sliced mushrooms to the skillet and cook for 5-6 minutes until they release their moisture and become golden brown.
Stir in the minced garlic and cook for 1 minute until fragrant.
Pour in the beef broth, Worcestershire sauce, and Dijon mustard. Stir well to combine and bring the mixture to a simmer.
Return the beef strips to the skillet and cook for an additional 5 minutes, allowing the beef to finish cooking and the sauce to thicken slightly.
Reduce the heat to low and stir in the sour cream until the sauce is smooth and creamy. Do not boil after adding sour cream to prevent curdling. Adjust seasoning with salt and pepper to taste.
Meanwhile, cook the egg noodles according to package instructions until al dente. Drain and set aside.
Serve the beef stroganoff over the cooked egg noodles and garnish with chopped fresh parsley.