Special equipment: an instant-read thermometer
Preheat the oven to 275 degrees F.
Allow the steaks to come to room temperature, 30 to 45 minutes. Season the steaks with some kosher salt. Heat a large, oven-safe skillet over medium-high heat until hot, about 2 minutes. Add the olive oil to the pan. Carefully place the steaks in the pan and allow them to sear untouched until golden brown, about 4 minutes. Flip the steaks and take the pan off the heat. Add the butter and thyme sprigs. Spoon the melted butter over the steaks and continue to baste for about 45 seconds. Transfer the skillet to the center of the oven and cook the steaks until an instant-read thermometer inserted into the thickest part reads 135 degrees F., 5 to 7 minutes for medium-rare.
Carefully remove the hot skillet from the oven, transfer the steaks to a cutting board and allow the meat to rest for 10 to 15 minutes. Slice the steaks and arrange on a serving plate. Spoon the remaining pan sauce over the steaks, sprinkle with sea salt and drizzle with olive oil.