Flatten the steak slightly using a rolling pin or meat mallet until about 1/3-inch thick.
Slice the beef into thin strips and season lightly with salt and black pepper.
Heat 1 tablespoon of vegetable oil in a large skillet over high heat.
Add half of the beef strips and sear quickly for about 30 seconds per side until browned. Remove and set aside.
Repeat with the remaining beef using the second tablespoon of oil.
Reduce the heat to medium-high and melt the butter in the same skillet.
Add the sliced onions and cook for 1 minute.
Add the mushrooms and cook until golden brown, scraping up the flavorful bits from the bottom of the pan.
Stir in the flour and cook for 1 minute.
Gradually pour in half of the beef broth while stirring continuously. Add the remaining broth and stir well.
Add the sour cream and Dijon mustard. Stir until smooth and combined.
Bring the sauce to a gentle simmer and cook for 3 to 5 minutes until slightly thickened.
Return the beef and any juices to the skillet.
Simmer for 1 minute, then remove from heat immediately to keep the beef tender.
Serve this Beef Stroganoff over egg noodles or pasta and garnish with fresh chives if desired.