Take the filets out of the refrigerator while the oven and skillet heat. They do not need to reach room temperature. Pat them dry, then season well on all sides with salt and pepper.
Preheat the oven to 425°F.
Heat the skillet over medium-high heat. Once it begins to smoke a little, add the oil and swirl it around the pan for about 15 seconds.
Add the filets to the screaming hot pan and sear on all sides (top, bottom, and all around the edges), 2–3 minutes per side. While searing the final side, add the butter, thyme, rosemary, and garlic to the pan. Baste the steaks constantly for the last 2–3 minutes.
Transfer the skillet to the oven. For the two 8-ounce center-cut filets this recipe was tested with, use about 5 minutes for rare, 6 minutes for medium rare, or 7 minutes for medium, turning halfway through. Use an instant-read thermometer as the final check because filet thickness, skillet heat, and oven accuracy can change the result.
Remove the skillet from the oven and transfer the filets to a plate to rest for at least 5 minutes before slicing.