Prepare the Steak: Flatten the steak to about 0.75cm (0.3 inch) thickness using a mallet or rolling pin. Slice into thin strips, around 0.5cm (0.2 inch) wide, trimming off excess fat. Sprinkle with salt and pepper.

Cook the Beef: Heat 1 tbsp vegetable oil in a large skillet over high heat. Add half the beef, spreading it quickly in a single layer with tongs. Sear for 30 seconds on each side until browned but still pink inside. Remove to a plate. Repeat with the remaining beef using the second tbsp of oil.

Cook the Vegetables: Reduce the heat to medium-high. Add the butter and melt it. Stir in the sliced onions and cook for 1 minute. Add the mushrooms and cook until golden, scraping the pan to lift any browned bits for added flavor.

Make the Sauce: Sprinkle the flour over the vegetables and stir for 1 minute. Gradually stir in half the beef broth, mixing until smooth. Add the remaining broth and stir in the sour cream and Dijon mustard. Combine well and bring the sauce to a simmer. Reduce the heat to medium-low and cook until the sauce thickens to a pouring cream consistency, about 3–5 minutes. Season with salt and pepper to taste.

Combine and Serve: Return the beef (along with its juices) to the skillet. Simmer for 1 minute, then remove from heat. Serve immediately over pasta or egg noodles, garnished with chopped chives if desired.