Remove the filet mignon from the refrigerator 25 to 30 minutes before cooking. Pat every surface thoroughly dry with paper towels.
Preheat the oven to 425°F (220°C). Place the cast iron skillet over medium-high heat for 3 to 4 minutes.
Season all sides of the steaks evenly with the kosher salt and black pepper.
Add the avocado oil to the hot skillet. Place the steaks in the pan with space between them and sear without moving for 2 1/2 to 3 minutes. Flip and sear the second side for 2 minutes. Briefly brown the edges with tongs.
Reduce the burner to medium-low. Add the butter, garlic, thyme, and rosemary. When the butter foams, tilt the skillet carefully and spoon the butter over each steak for about 30 seconds.
Transfer the skillet to the oven. Begin checking after 4 minutes and continue cooking as needed until the thickest part of each steak reaches 145°F (63°C) for the USDA safe minimum temperature.
Transfer the steaks to a warm plate, spoon over a little pan butter, and rest for at least 5 minutes before slicing.
Serve whole or slice across the grain. Spoon over additional garlic-herb butter if desired.