Prepare the Beef: In a large skillet, heat vegetable oil over medium-high heat. Add the beef strips, season with salt and black pepper, and cook for 3-4 minutes, until browned on all sides. Remove the beef from the skillet and set aside.
Cook the Vegetables: In the same skillet, melt butter over medium heat. Add the chopped onion and minced garlic, cooking until softened, about 2-3 minutes. Add the sliced mushrooms and cook for an additional 5 minutes, until the mushrooms are tender and lightly browned.
Prepare the Sauce: Stir in the Dijon mustard, paprika, and flour (if using). Cook for 1 minute to allow the flour to absorb the flavors. Gradually add the beef broth, stirring constantly to prevent lumps. Bring the mixture to a simmer and cook for 3-5 minutes, until the sauce begins to thicken.
Combine and Finish: Return the beef to the skillet, stirring to combine. Reduce heat to low and add the sour cream, stirring until the sauce is smooth and creamy. Let the mixture simmer for another 2-3 minutes to warm through. Adjust seasoning with salt and pepper as needed.
Serve: Serve the Beef Stroganoff over cooked egg noodles, rice, or mashed potatoes. Garnish with fresh chopped parsley for an added touch of color and flavor.