There are as many ways to bake or roast beef tenderloin as there are chefs--some favor the high heat method, others opt for a searing followed a low roast approach--but the simplest way to cook this delicious and expensive cut of meat is the slow-roast, low heat method.
Most beef tenderloins are fully trimmed by the butcher and naturally have little fat, but occasionally a thin layer of silver skin--it looks like a thin, striped layer of white skin--remains that must be cut away, as it causes the meat to shrink. Simply put the point of knife under the skin, slide the edge of the knife away from you and cut off the silver skin.
Tie the roast to prevent flattening during cooking. If the roast tapers at one end, tuck the small end back under the roast to achieve a uniform thickness. Using butcher's string, tie the roast firmly every 3 inches, but not so tight as to cause the meat to be squeezed, looping the string under the roast, tying a simple knot and cutting any long ends of string.
Take the roast out of the refrigerator 30 minutes before roasting and leave covered at room temperature. Preheat the oven to 250 degrees.
Rub the roast sparingly with olive oil, then sprinkle the roast generously on all sides with coarsely ground pepper and kosher salt. Or spread the roast with a thin layer of Dijon mustard thinned with a little olive oil, sprinkle with the salt and pepper and tuck several fresh thyme sprigs under the roast in the pan.
Place the probe of the digital thermometer into the end of the roast, keeping it in the center of the roast, parallel to the pan, and set the digital thermometer for 135 degrees for medium rare, 145 degrees for well done--the meat will continue to cook for 15 minutes after it leaves the oven, raising the internal temperature 5 to 10 degrees.
Cook the roast for approximately 20 minutes per pound, but be aware that larger roasts may take longer--that's why a digital thermometer with an alert feature makes this so much easier. If using a simple meat thermometer, check the temperature every 15 minutes or so. When the roast reaches the target temperature, remove and let rest under a sheet of aluminum foil.