Season the sliced beef with salt and black pepper. Coat the beef strips lightly with the flour.

Warm the butter and olive oil in a large skillet over medium heat. Add the mushrooms and onion, cooking until softened and browned.

Move the mushrooms and onion toward the edges of the skillet. Place the floured beef in the center and sear briefly until browned, taking care not to overcook it.

Add the minced garlic and cook briefly until fragrant. Pour in the beef broth and Dijon mustard, then simmer gently until the sauce has reduced slightly.

Take the skillet off the heat and mix in the sour cream until the sauce becomes smooth and creamy. Do not bring the sauce to a boil after adding the sour cream. Adjust the salt and black pepper to taste.

Serve the beef stroganoff immediately over buttered egg noodles, mashed potatoes, or steamed rice. Finish with chopped fresh parsley if desired.