Sprinkle the filet with salt and pepper. To a heated pan add the oil, salt and pepper. Brown the meat on all sides. Place into a 350 degrees F. oven for 30 to 35 minutes, or until the meat thermometer registers 120 degrees F. to 125 degrees F. (for rare). Transfer to a cutting board and let rest for 10 minutes, covered loosely with foil.
Make the sauce while the beef is resting. Pour off the fat from the pan, add the Madeira, and boil it, scraping up the brown bits, until it is reduced to about 2 tablespoons. Add the broth and boil the mixture, stirring for 1 minute. Stir the arrowroot mixture, add it to the skillet, whisking, and simmer the sauce, whisking, for 1 minute.
Slice the filet and transfer to a platter. Spoon sauce around the meat and serve the remaining sauce separately. Sprinkle with chopped parsley.