Filet mignon, the most tender beef cut of all, is an expensive cut of meat often reserved for special occasions. A lean steak measuring up to 2 inches thick, filet mignon comes from the tenderloin of the beef, located between the sirloin area and the ribs. Tender cuts such as filet mignon and porterhouse and T-bone steak are best cooked to medium-rare, using high-temperature cooking methods such as broiling.
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Thaw frozen filet mignon. Refrigerator-thawing, which may take up to 24 hours for thick steak, is the safest method. If you don't have time to thaw filet mignon in the refrigerator, thaw it in cold water: Place the meat in an airtight package, then submerse the package in a bowl of cold water. Pour out the water and replace it with fresh water every 30 minutes. Thawing in cold water takes 2 to 4 hours, depending on the thickness. Never defrost filet mignon at room temperature.
Remove the steak from the refrigerator 20 minutes before cooking to allow the steak to warm to room temperature. Don't allow the steak to remain out of the refrigerator any longer, as bacteria may develop. Warming the steak to room temperature promotes even cooking, especially with thick cuts of meat.
Place an oven rack about 4 to 6 inches below your oven's heating element. Turn the oven on broil and allow the oven to preheat for at least 15 minutes.
Place a heavy cast iron skillet or a broiling pan in the oven and allow it to heat.
Rub the filet mignon generously with extra-virgin olive oil, then sprinkle the meat with freshly ground black pepper.
Remove the hot pan carefully from the oven. Place the meat carefully in the pan.
Return the pan to the oven, then broil the meat quickly for 3 to 4 minutes on each side. Turn the meat with tongs, as using a fork allows meat juices to escape.
Turn the broiler off, and then set your oven temperature at 500 degrees F without removing the pan from the oven. If you prefer a rare filet mignon, use a meat thermometer to ensure the center of the meat reaches a safe temperature of at least 135 degrees F, which takes from 1 to 5 minutes, depending on thickness. For medium, cook filet mignon for 2 to 7 minutes -- until the meat reaches a temperature of at least 140 degrees. For a steak cooked medium-well, cook filet mignon for 4 to 9 minutes -- to a temperature of at least 150 degrees. Turn the filet mignon once about halfway through the cooking time.
Remove the filet mignon from the oven and place it on a carving board. Cover the meat loosely with aluminum foil, then allow it to rest for 5 to 10 minutes.
Carve the meat, and then transfer it to a warm serving platter. Sprinkle the filet mignon with sea salt or kosher salt, and then serve.