Position a rack in the bottom third of an oven and preheat to 425F degrees (220C).
Butter the ends and bottom of the beef fillet and place in a small, heavy roasting pan (without a rack) in which it fits comfortably. Sprinkle with salt and pepper. Place in the oven and roast until an instant-read thermometer inserted in the center of the meat registers 120 F degrees (49C) for rare or 130F degrees (54C) for medium-rare, 20-30 minutes. Transfer to a warmed serving plate and cover loosely with a piece of aluminum foil to keep it warm. It will continue to cook a little.
Using a large spoon, skim off the fat from the pan juices. Place the pan over medium-low heat and add the shallots. Cook, stirring, until translucent, 3-4 minutes. Add the water, raise the heat to medium and stir, scraping up any browned bits stuck to the pan bottom. Add the Madeira, bring to a boil over medium heat and boil until reduced by about one-half. Combine the cornstarch mixture and the cream and stir until blended. Add to the pan and quickly stir into the juices. Cook, stirring, until slightly thickened, 1-2 minutes. Season to taste with salt and pepper.
Cut the strings on the fillet, then remove the strip of fat tied to the top of the fillet and discard. Using a very sharp, thin-bladed knife, slice the meat crosswise into 12-14 slices, each about 1/2-inch (12 mm) thick. Spoon a little of the sauce onto each warmed plate and place 2 or 3 slices of meat on the sauce. Spoon the remaining sauce over the meat, garnish with the chopped parsley and serve.