Heat oven to 250 degrees F and place rack in middle position.
Pat steaks dry with a paper towel, then season with salt and pepper. Place on a wire rack inside a rimmed baking sheet, and bake for 30-50 minutes, flipping half way, until internal temperature registers 90 degrees F.
Heat oil in a large skillet, over high heat, until just smoking.
Remove steaks from pan, and pat dry with a paper towel.
Place in the hot pan, and do NOT move them. Let cook for 30 seconds. Flip and cook 30 seconds on the other side, and continue to do this, flipping them every 30 seconds until lightly browned, about 3 minutes.
Push steaks to the side, and add butter, let it melt and add shallots, garlic, and thyme. And tilt the pan so the butter pools and aromatics are sitting in it. Use a spoon to baste the steaks with the butter, and continue to do this, flipping the steaks every 30 seconds or so until you reach desired internal temp (125 degrees), 1-3 minutes.
Remove steaks from pan, set on carving board, and let rest for 10 minutes.
Slice, and serve with the pan butter (strain out the aromatics).