Allow the steak to rest at room temperature for 35 minutes before cooking.
Heat a large cast-iron skillet over high heat. Meanwhile, generously sprinkle the steak on all sides with salt and pepper. Once the skillet is hot, add the butter and oil and swirl until the butter melts.
Once the butter begins to foam, place the steak in the skillet and sear for 4 minutes. Flip the steak and add the thyme and garlic to one side of the skillet. The thyme will pop and fry in the butter and oil, then will settle in a few seconds. Cook until a thermometer inserted in the thickest part of the steak registers 120 degrees F, about 4 minutes, then tilt the skillet a bit to collect the butter and oil and use a large spoon to baste the steak. For a medium-rare steak you can cook 4 more minutes, then remove it from your skillet at 125 degrees and let it rest for 10 minutes to reach 135 degrees F.
Carve the meat off the bone and slice the steak into strips. Sprinkle with the flaky salt and the fried thyme sprigs and serve.