Any leftovers are fabulous for sandwiches.
Trim meat, removing excess fat and silver skin. Cut off about 4 inches of narrow end, about 1 pound, and reserve for another use.
Place fillet on large sheet of parchment paper. Dust all over with salt, using 3/4 teaspoon salt to a pound of meat. Roll in peppercorns. Tie with butcher’s string at 2-inch intervals. Wrap meat in parchment loosely, and refrigerate at least 24 hours and up to 48 hours.
Remove fillet from refrigerator an hour before cooking. Rub all over with oil. Heat oven to 400 degrees. Sear fillet on all sides in a heavy roasting pan over two burners, under broiler or on grill. Or cut in half and sear in two pieces in large, heavy skillet.
Place in oven in roasting pan. Roast 15 minutes. Test with instant-read meat thermometer: if thickest part registers about 105 degrees, meat will be very rare when finished. For medium rare, roast 20 to 25 minutes, until thermometer registers 115 degrees. For medium, roast longer, to 125 degrees. At these temperatures, meat will be slightly undercooked, but will continue to cook after it is removed from oven. Place meat on cutting board. Allow it to rest 10 to 15 minutes.
Remove string, cut meat in 1/2-inch thick slices, arrange on a platter, and serve.