Preheat a cast-iron skillet over high heat until hot.

Just before cooking, pat steak dry with paper towels and sprinkle with salt and pepper. Add oil to hot skillet then add steak. Cook steak for about 4 minutes, or until dark brown and caramelized on the bottom.

Turn steak over and cook for 2 minutes. Reduce heat to medium-high. Add butter, garlic, and thyme to skillet. Cook steak, using a spoon to basted melted butter over steak as it cooks, for about 2 more minutes for medium-rare doneness.

Transfer steak to carving board and let rest for about 4 minutes (half the cooking time).

Using a sharp knife, slice each steak against grain on a bias. Divide steak among 2 plates and serve.