Remove the filets from the refrigerator at least 30 minutes before you intend to cook them. Salt and pepper the filets, or, if you prefer, you can simply salt them, without adding pepper. Allowing the meat to come to room temperature allows the muscle fibers to relax. Arguments for and against salting the filets each have their merits. You don't want to salt the filets right before you cook them, because that will pull the moisture out of the meat, making it dry. And the delicate filet mignon has very little fat, so you don't want to dry it out. You can salt the steaks a couple of days before you cook them, which will soften the steak. Use coarse kosher or sea salt, for a better flavor.

Place as many bacon strips as you have filets into a cold skillet. Turn the heat to medium and heat the bacon gently, to retain its flexibility. You want fat on the bacon. Blot the bacon with paper towels. You can also put uncooked bacon directly on the filets, because you want as much fat as possible to protect the delicate steak from drying out while you cook it.

Wrap a strip of bacon around the circumference of each filet and secure it with a toothpick that you stick sideways through the bacon ends and into the filet. Using raw bacon allows more of the fat to tenderize the meat, which is known as barding, because the layer of bacon on the outside keeps the filet from drying out.

Brush your stove top grill pan with a pastry brush dipped in olive oil or butter. Heat the grill to medium high. Lightly grease your pan, using butter or olive oil, but do not allow the butter or olive oil to burn.

Place the fillets on the medium-hot grill and pan-sear them for 4 to 7 minutes without moving them. Flip the filets with tongs and cook them for another 4 to 7 minutes without moving them. Aim for 4 minutes a side so that you don't overcook them. You can cook them longer if they aren't cooked to your desired doneness. Don't let the butter or olive oil smoke, because the fats will break down and possibly become toxic.

Check the doneness of the filets after cooking them on each side by inserting the tip of an instant-read thermometer into the thickest filet. Meat keeps cooking after it is taken off the heat, so remove the filets from the grill pan at 130 F for very rare, 140 F for rare, 145 F for medium rare and 160 F for medium. According to FoodSafety.gov, you should cook whole cuts of beef to 145 F and then let them rest for 3 minutes.

Since the filet mignon is considered the tenderest cut, you don't want to ruin its texture by cooking it beyond medium-rare or medium. Let the filets rest for 5 minutes before serving. The filet mignon will continue to cook while it is resting. It is best to discard the bacon before serving the filets. The purpose of using bacon is merely to keep the filet moist. If cooked to perfection, you can cut filet mignon with a fork, because it can be as tender as butter.