1. Let steaks stand 30 minutes at room temperature.
2. Sprinkle salt and pepper evenly over steaks. Heat a large cast-iron skillet over high heat. Add oil to pan; swirl to coat. Add steaks to pan; cook 3 minutes on each side or until browned. Reduce heat to medium-low; add butter, thyme, and garlic to pan. Carefully grasp pan handle using an oven mitt or folded dish towel. Tilt pan toward you so butter pools; cook 1 1/2 minutes, basting steaks with butter constantly. Remove steaks from pan; cover loosely with foil. Let stand 10 minutes. Reserve butter mixture.
3. Cut steak diagonally across grain into thin slices. Discard thyme and garlic; spoon reserved butter mixture over steak.