Prepare the beef:
Toss the thinly sliced beef with flour, ensuring each piece is lightly coated. This helps thicken the sauce later.
Cook the beef:
Heat olive oil or butter in a large skillet over medium-high heat. Add the beef slices and cook until browned on all sides, about 2–3 minutes per side. Remove the beef from the skillet and set aside.
Sauté the vegetables:
In the same skillet, add the onions and cook until softened, about 3 minutes. Add the mushrooms and cook until browned and their liquid has evaporated, about 5 minutes. Stir in the minced garlic and cook for 1 more minute.
Make the sauce:
Pour the beef broth into the skillet, scraping up any browned bits from the bottom. Stir in the Dijon mustard and Worcestershire sauce. Bring to a simmer and let cook for 5 minutes, allowing the flavors to meld.
Add the sour cream:
Reduce the heat to low and stir in the sour cream until the sauce is creamy and smooth. Do not boil to prevent curdling.
Return the beef:
Add the browned beef back to the skillet and stir to coat it in the sauce. Simmer for 2–3 minutes until heated through.
Serve:
Serve the beef stroganoff over cooked egg noodles, rice, or mashed potatoes. Garnish with fresh parsley if desired.