Regardless of whether you will be broiling, grilling or pan-searing your filets, there are a few tips that apply universally. Start by selecting a good steak. Choose filets that have a lighter color, indicating that they are better marbled. If your filets are extremely lean, consider wrapping them in suet or bacon to add some fat and prevent them from drying out. Season filets before you cook them. Simply adding a bit of salt and pepper will improve the flavor of the steak without changing it. Finally, let the steak reach room temperature before you cook it.
Pan-sear, broil or grill your steaks as quickly as possible on as high a heat as possible. Slow cooking will dry out a filet mignon. Ideally the filet should be cooked rare or medium-rare. When cooked to higher degrees of doneness, filet mignon will both lose its tenderness and its moisture.
Although many recommend a meat thermometer as a test of doneness, it's also possible to just use your senses. A trick that chefs use is to press the steak with their finger to feel how much give or springiness it has. You can use your face as a guide. If the steak feels like your cheek, it is rare, and if it feels like your earlobe, it is medium rare. Medium steaks have a texture similar to the side of your nose, and medium well will feel like the tip of your nose. When in doubt, pull the steak off the fire too soon rather than too late. Not only is it easier to recook a steak, but the steak will also continue cooking for a few minutes even after being removed from the heat.
To cook the filet mignon, place it on a broiling pan, grill grid, or in a good quality stovetop pan and spray it with a high-temperature oil or non-stick spray. Ensure that the pan is preheated to the hottest possible temperature -- many restaurants cook filet at temperatures over 1000 degrees. Once the sides of the steak begin to turn gray, flip the steak over and cook the other side. Use the texture test outlined above to determine doneness and remove the steak from the heat when it is done. Let it rest five minutes at room temperature before serving. Enjoy!