Using a sharp knife trim all white membrane and fat from filets.
Wrap a slice of bacon, slightly stretching as you wrap, completely around filet and secure with a piece of cotton butcher's twine or a toothpick.
Season heavily with salt and pepper on both sides of the filets.
Heat a cast iron skillet or any heavy bottom skillet over medium high heat. Add the butter and oil. When it starts to slightly smoke add the steaks. Sear on each side for 2 minutes.
Transfer the skillet and filets to the oven and roast for 6-7 minutes. Check for desired doneness (see temps below in Notes).
Filet mignon are cut from beef tenderloin and typically cut 1 to 2 inches (2.5 cm to 5 cm) thick and 2 to 3 inches (5 cm to 7.6 cm) in diameter. Most often, you'll find them sold in 6 to 8 ounce portions, but they can also be found in 10, 12, or even up to 16 ounce portions.
Internal Temperature Guide for Filet Mignon
The USDA recommends a safe minimum internal temperature of 145° F. for any type of steak (beef, veal, pork, etc.). This translates to a steak of medium doneness. However, here are internal temperature ranges to consider.Keep in mind that steaks will continue to cook as they rest after removing them from the heat source. This can increase the internal temperature by 3 to 5 degrees F.
Rare- 120 to 125° Fahrenheit
Medium rare- 130 to 135° Fahrenheit (54°Celsius)
Medium- 140 to 145° Fahrenheit
Medium well- 150 to 155° Fahrenheit
Well done- for a filet mignon with no signs of pink left, the internal temperature should be 160° Fahrenheit or higher