Heat a large cast-iron skillet over high heat for 5 to 7 minutes.
Meanwhile, pat dry the filets mignons with paper towels. Brush the filets lightly all over with the oil. Combine the fleur de sel and cracked pepper on a plate and roll the filets on all sides in the mixture, pressing lightly to help the salt and pepper adhere. The steaks should be evenly coated with the salt and pepper.
When the pan is extremely hot, add the steaks and sear evenly on all sides (top, bottom, and sides) for about 2 minutes per side. (Be sure the cooking area is well ventilated.) You'll probably need about 3 turns to sear the sides and about 10 minutes total.
Remove the pan from the heat and arrange all the filets flat in the pan. Top each with a tablespoon of butter, then place the pan in the oven. Cook the filets for 8 to 12 minutes to 120 degrees for rare and 125 degrees for medium-rare. Remove the steaks to a platter, cover tightly with aluminum foil, and allow to rest for 5 to 10 minutes.
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