Pat steaks dry. Season generously with salt and pepper 30 minutes before cooking.
Preheat the oven to 400°F and position a rack in the center.
Heat a cast-iron skillet over medium-high heat until very hot; add the oil.
Sear steaks 2-3 minutes per side until a deep brown crust forms. Add butter, garlic, and herbs in the last minute and baste.
Transfer the skillet to the oven. Roast 6-8 minutes for medium-rare.
Pull filets from the oven at your target pull temp (see chart above) — for medium-rare, 125-130°F — then transfer to a warm plate.
Rest the filets (see Notes).