Cut the beef into thin, 2 x 1/4-inch strips. Season with salt and pepper.
Heat 2 T of oil in a large, heavy skillet over med-hi heat. Add the meat and sear for approximately 1 minute on each side or until just browned. Remove from the skillet with a slotted spoon and keep warm.
Add the remaining 1 T oil to the skillet and heat. Add the mushrooms, carrot, and onion and sauté until the mushrooms give up their juice, about 8 minutes.
Return the beef to the skillet and stir in the wine and broth. Continue to sauté until the meat is just done, 1 to 2 minutes for rare. Stir in the butter until just melted. Season to taste with salt and pepper. Serve immediately.