Season the filet mignon liberally with sea salt and black pepper on all sides.
06Heat a large cast iron skillet over medium-high heat for 2-3 minutes, until very hot. Add the remaining butter (1 tablespoon or 14g) and let it melt.
07Add the steaks to the pan in a single layer. Sear for 2 minutes on each side, without moving them around.
08Transfer the skillet to the preheated oven. Cook filet mignon in the oven to the doneness you want. (I recommend medium rare or medium.) For a 2-inch (5 cm) thick filet, it takes about 5 minutes for rare, 6 minutes for medium rare, 7 minutes for medium, or 8 minutes for medium well.For best results, use a meat thermometer to check for the right temperature -- 120 degrees F (52 degrees C) for rare, 130 degrees F (54 degrees C) for medium rare, 140 degrees F (60 degrees C) for medium, and 155 degrees F (68 degrees C) for medium well. The temperature will rise by another 5 degrees F while resting (see next step).
09Transfer the steaks to a plate. Top each with 1/2 tablespoon of garlic herb butter (slice the log of herb butter into four parts and place one on each steak). Let the steaks rest for 5 minutes before serving and slicing.